It really is a debatable topic. Hasegawa is widely respected as far as I know. While I wouldn't call his theory that the Soviet Invasion of Manchuria, not the atomic bombs, is what caused Japan's surrender "widely accepted" I wouldn't call it a fringe theory either. Geoffrey Jukes, a military historian, wrote a review of Hasegawa's book "Racing the Enemy" and said that he agreed with Hasegawa's conclusions and to quote him

the author’s diligent research in the Japanese sources demonstrates conclusively that it was the Soviet declaration of war, not the atomic bombs, that forced the Japanese to surrender unconditionally

The review can be found here. http://miskinhill.com.au/journals/asees/22:1-2/reviews/hasegawa-racing-enemy

However, I know quite a few historians who would disagree with Hasegawa's conclusion. For example Edward J. Drea, one of the best historians on post Meji Japan, argues that it was indeed the Atomic Bombs that caused the downfall of Imperial Japan's Army and had the greater impact on the morale of the IJA. In his book "Japan's Imperial Army: Its Rise and Fall" he argues that:

For the Army leaders, the atomic bomb was the greater shock because, lacking a military countermeasure, they could no longer continue to fight in expectation of gaining more advantageous conditions to end the war

There is definitely merit to both theories. On the one hand Japan did hope to use the Soviet's as intermediaries, and so the Soviets breaking the non-aggression pact and invading, certainly came as a shock and a blow to national morale. The Soviet invasion also destroyed the Kwantung Army, one of Imperial Japan's biggest armies (it had also once been the most well trained, but many of its most experienced officers and units had been withdrawn and replaced with conscripts).

But on the other hand Japanese military intelligence had identified that the Soviets were building up their military on the border with Manchuria and guessed that by Spring 1946 the Soviets would attack, so the actual deceleration of war wouldn't have been unexpected. Also, as Drea points out the atomic bombs signaled a new age of warfare, one that Japan's army leaders knew they couldn't fight. The Soviets ,for all their strength, were a conventional enemy that the Japanese had fought before. The same can not be said for the Atomic Bombs. Nobody had seen a weapon of such magnitude and such power. Some people will point out that Japan's cities had been firebombed and thus an Atomic Bomb wouldn't be that devastating. The problem with this idea is that conventional bombing can be avoided and the damage mitigated and also it takes a large amount of planes and manpower to completely destroy a city; the atomic bombs vaporized two cities within a heartbeat.

Another important factor is Hirohito himself. The Imperial War council was split on whether to surrender or not, Hirohito broke the stalemate and came out in favour of ending the war. He wrote down his rational and to quote him:

Moreover, the enemy has begun to employ a new and most cruel bomb, the power of which to do damage is, indeed, incalculable, taking the toll of many innocent lives. Should We continue to fight, not only would it result in an ultimate collapse and obliteration of the Japanese nation, but also it would lead to the total extinction of human civilization.

Hirohito had always been concerned with the survival of the Imperial Throne and he was concerned that allowing the war to go on longer and thus allowing the Americans to drop more atomic bombs would hurt the Japanese public's opinion of the monarchy.

Finally, many in the Japanese high command had express doubt that the Soviets would actually help them negotiate with the West. The Japanese strategy had always been to cause as many allied casualties as possible and thus force a favorable peace treaty; however the atomic bomb took away that ability and force Japan to see that they could no longer continue.

Sources:

Embracing Defeat by John Dower

Japan's Imperial Army by Edward Drea

Hirohito and War by Pete Weltzer

I personally am not aware of any commentary on Hasegawa's work, but I wouldn't dismiss it out of hand as others did.

The politics of the Japanese high command were so convoluted and so contradicting that a decision like surrender would have been very difficult. Namely, this was primarily due to the Army. Because the Navy had been all but destroyed, with its last sortie (Ten-Go) being shattered and its fleet remnants annihilated at Kure and Sasebo, the only faction that had any political power was the army. And the army, despite grievous losses, was still more or less a coherent unit. There were still many troops in China fighting that could be redeployed in case of an American invasion of the homeland, and there were also a large army in the Home Islands themselves, ready to fight against invaders. Thus it was of little surprise that the Army had a great deal of political power, on top of its ability to essentially disband any government that it disagreed with (as a government was required to have a serving Army officer on the cabinet, the Army could simply forbid any of its members from serving on the cabinet).

The Soviet invasion did two things: firstly, the Soviets entering the war ruined all hope for Japan to use the USSR as an intermediary for peace. The real putz, however, was the imminent destruction of all Japanese forces in China. The Kwantung Army that defended Manchuria had been severely weakened as over time units were siphoned away, making them no match for the battle-hardened heavily mechanized Soviet troops. The thing is those mechanized troops move QUICKLY. They were in a position to cut off all the Japanese troops in China from supply, as well as directly invade Korea. This broke the power of the Army, as a huge amount of its ability to fight had been threatened and crippled.

Most of the other ministers had already argued to surrender long before the bombs were dropped. As the army had lost face at last, I can see Hasegawa's argument, that the Soviet invasion was the breaking point for Japan, would make sense,

If you read stuff written by the Japanese decision makers at the time it becomes obvious that it was the Soviet entry into the war that was the deciding factor. Particularly for the army. So among historians in Japan, Hasegawa's position is pretty common.

The atomic bombings influenced events but it was secondary (considering that 60+ cities were already fire bombed, the loss of another 2 cities wasn't going to change the minds of the crazy army leaders). The navy and the civilians already knew the war was lost so the bombs helped to make their case. But the army was the last hold out and to get the army leaders to change their minds, you had to smash the Japanese armies in China, which the Soviet would do.

4 primary Japanese source materials are: Foreign Ministry (ed), Shuusen shiroku (6 vols), 1952; General Staff (ed), Haisen no kiroku, 1967, republished in 2005; Kashima research institute (ed), Nihon gaikoshi vol 25: Daitoa senso, shuusen gaikou, 1972; Eto Jun (ed), Shuusen kousaku no kiroku (2 vols), 1986

Among American historians this is still contested. It's not surprising because in public relations, the Japanese government used the atomic bombs as the main excuse for the surrender. (The Japanese government didn't want to admit the influence the Soviets had on the decision because this would then invite Soviet meddling in the postwar order. If Japan was going to surrender, it was preferable that Japan surrender to the U.S. alone and not be divided like West Germany and East Germany.)

Final point that I want to make: I think many historians are missing the importance of US accepting Japan's counter on August 10th to the Potsdam Declaration. "客日二六日附三国共同宣言ニ挙ゲラレタル条件中ニハ日本天皇ノ国法上ノ地位変更スル要求ヲ包含シ居ラザルコトノ了解ノ下ニ日本政府ハ之ヲ受諾ス" Translation: "The Japanese government accepts the Joint Declaration made on the 26th past [meaning July 26th] by the three countries with the understanding that the it does not include a demand on changing the Japanese Emperor's position within national law." Since the US took Japan's response as sufficient, the leaders of the Japanese government assumed that the imperial institution was safe. This was the last key necessary for the surrender of Japan.

The US reply sent on 12 August was: Surrender and be subject to the authority of the allies. But in the case of the imperial institution, "The ultimate form of government of Japan shall, in accordance with the Potsdam Declaration, be established by the freely expressed will of the Japanese people." And for Japanese leaders that was enough. After some more debates and an attempted coup, on August 15th Japan surrendered.

Edited for clarity by adding "Japanese" in front of government in paragraph 4.

The bomb historians I have talked about this with have all more or less accepted the argument that the Soviet invasion of Manchuria was extremely influential to the final Japanese decision to surrender, at least as important as the bombings. Some go further and are compelled completely by Hasegawa, but they don't strike me as the majority. Some don't go that far and reserve space for the bomb to matter.

For what it's worth, as a scholar of these things, what I think Hasegawa does extremely well is to set up the context of the Japanese-Soviet negotiations and why the Soviet invasion would have mattered a lot to the Japanese high command. It is the best discussion of the US-Soviet-Japanese situation that I have seen.

But I don't really see how he can say that the invasion mattered more than the atomic bombs. It's just not really in the text. He has a lot of context, but no "kicker" argument that proves the final point. I find it entirely reasonable to conclude that they both had a big effect — which is indeed what the sources he quotes seem to indicate for the most part. This is, of course, an entirely separate question from the one he poses at the end about whether the war could have been ended without a US invasion and without the use of atomic bombs (just because the atomic bombs may not have been necessary because of lots of other factors doesn't mean that they didn't have an influence).

That being said, the argument that it was the bombs that mattered and not the Soviets is based on some rather tenuous evidence as well (coincidences of timing which apply equally well to both, a few statements from Hirohito which could have had multiple motivations behind them, etc.). So I'm not saying it is cut and dry in any respect. Most of the assertion that the bombs were what Japan to surrender have been just that — bald assertions without any evidence other than timing (which of course is exactly the same for the Soviet invasion).

My experience is that the only people who think Hasegawa is not worth taking seriously at all are people who have not read his book. Or read very many books on the subject at all. Unfortunately the scholarship on the bomb has moved well beyond the debates of the mid-1990s (e.g. the Smithsonian Enola Gay exhibit controversy) but the latter debates are still what dominate the popular discussion of it.

The first rule of politics in war is that war is never about one thing.

The idea that either the two nuclear bombs, or the Soviets move on China and Korea were the thing to end the war are both nonsense because war is in itself a negotiation of ideals and philosophies between many people. While it may be easy to say that two nuclear bombings were reasonably unremarkable- after all, this wasn't the first time a Japanese city was practically obliterated by air attack- it's equally easy to say that the Soviets couldn't be the nail that seals the coffin because the Japanese were not ignorant of Soviet fighting strength.

What made the Soviets important was the reaffirmation that the Japanese didn't really have anywhere to run.

What made the nuclear bombs important was the idea that the Japanese needed to surrender ASAP.

The idea that either of these things was the thing that made it happen is ludicrous. Wars don't start and stop over one thing. You need to take a few steps back to get the entire picture in the frame.

Robert Pape offers an alternative view, not entirely different to Hasegawa's.

The principal cause of Japan's surrender was the ability of the United States to increase the military vulnerability of Japan's home islands, persuading Japanese leaders that defense of the homeland was highly unlikely to succeed. The key military factor causing this effect was the sea blockade, which crippled Japan's ability to produce and equip the forces necessary to execute its strategy. The most important factor accounting for the timing of surrender was the Soviet attack against Manchuria, largely because it persuaded previously adamant Army leaders that the homeland could not be defended. Contrary to the assertion of the Strategic Bombing Survey that bombing was so effective that even if there had been no atomic bomb, Soviet attack, or planned American invasion, surrender would have occurred at nearly the same time, in actuality the naval blockade, invasion threat, and Soviet attack ensured that surrender would have occurred at precisely the same time even if there had been no strategic bombing campaign.

Pape disputes the idea that the atomic bombs or threat of more atomic destruction was the cause of Japanese surrender, as the conventional strategic bombing of Japanese cities had already achieved so much, that atomic bombing wouldn't do drastically more damage, the phrase 'the hostage is already dead' is used. He argues quite like Hasegawa that it was military vulnerability not civilian, which forced Japan to surrender. This was due to the Japanese leadership no longer believing they could stop the Home Islands from being invaded and overrun. The three reasons Pape offers for this change of opinion were(in descending importance):

• Most important was that the Allied sea blockade had completely cut off all outside sources of supply, crippling the key economic and military pillars supporting Japan's strategy.

• The fall of Okinawa, putting American tactical air power in range of the southernmost Home Island of Kyushu.

• And least of all the destruction of the Japanese armies in Manchuria due to the Soviet invasion.

However much I enjoy Pape and Hasegawa's arguments, I find they underestimate the huge affect the atomic bombs had on Japanese morale. Whilst Pape argues from a very mathematical view concerning destruction of cities, it doesn't give enough attention to morale destroying affects of the Allies producing the ultimate super-weapon.

Sources: Robert A. Pape 'Why Japan surrendered' International Security, Vol. 18, No. 2 (Autumn, 1993), pp. 154-201

The Myth of Nuclear Deterrence

In this talk, Ward Wilson makes the argument that large scale slaughter of civilian populations has historically never caused a warring party to surrender and concludes that it is unreasonable to assume that using an atomic bomb instead of a fire or a mongol horde makes a difference without explaining why. It also contains quite a bit of data on the Japanese and other historical city destructions (I'm sorry, the slides are not readable, I have seen a better version but can't find it) and in the end comes to the same conclusion as Hasegawa.

Independent of whether you believe that the Soviet invasion caused the Japanese to surrender, if you want to defend the theory that it was because of the use of atomic bombs you need to explain convincingly why destroying cities with atomic bombs instead of chemical bombs is different, though both methods are equally effective.

I think you might find the comments to that video remind you of the "non-sourcing, uneducated and insulting redditors". I have not yet heard any convincing argument against the conclusion.

Edit: I found a version with readable slides: https://www.youtube.com/watch?v=6BFyfK43mEk