I’m not sufficiently expert in this topic to address it but it’s perhaps worth noting that Haganah wasn’t a minority faction like the Stern Gang and the Irgun. It was the primary paramilitary force of the Yishuv and ultimately it answered to the mainstream political leaders like Ben Gurion and is the direct forerunner of the IDF. Its relations with the other groups varied over time, in particular with greater cooperation after the end of WWII. I’m not familiar the details of each of the incidents you refer to but, the King David Bombing for instance, while carried out by Begin and the Irgun, was ordered and approved by Haganah. That they immediately disavowed and condemned the attack (despite their involvement in it) I think gives some indication of what they expected the wider public reaction to be.

edit: some typos.

It's worth noting that pretty much none of the incidents you describe were Haganah-involved.

The King David Hotel attack was carried out by Irgun. While the Haganah approved the plan initially, it had canceled that approval by the time the attack went out. The Haganah had no involvement in the attack.

Destroying bridges was carried out by the Haganah, but attacking bridges to hamper the British army does not qualify as "terrorism" in the modern use of the term, which relates to attacks targeting civilians or meaning to inspire fear among civilian populations. The "Night of the Bridges" targeted British army infrastructure and supply routes.

The letter bombs to British cabinet members was the work of the Stern Gang (Lehi).

The assassination of Lord Moyne was done by Lehi.

I'm not sure what you're referring to regarding the bomb in a baby carriage.

The general Jewish population was by and far away most supportive of the Haganah. It was the Haganah that formed the backbone of the IDF when it was formed during war, and it was the Haganah that had the largest number of members, fighters, and supporters. It was also the Haganah that raised the largest amount of funds from Jews abroad, and fielded the most support from them. It was also the Haganah that had the best relations with Zionist and Jewish groups based abroad.

Indeed, it was also the Haganah that sought to arrest its competition, and often cooperated with the British to do just that. One of the more famous moments in early Zionist history was known as the Saison (hunting season). Not long after Menachem Begin took charge of the Irgun, the Irgun leadership decided that WWII was all but over (it was around August 1944) and decided that they could resume targeting the British. Lehi, of course, never stopped doing so, but they were far smaller even than Irgun. But when Irgun resumed operations against the British, the Haganah and Jewish Agency Executive condemned both groups and tried to persuade them to end their attacks on the British, at least until the war ended. Surprisingly, after assassinating Lord Moyne, Lehi acquiesced to this request, but Irgun did not. So the Haganah declared a Saison on Irgun operatives.

In short, the Haganah spent November 1944 to March 1945 tracking down Irgun members, confiscating their weapons, interrogating them for information, and often beating them. They even handed some over to the British police. With the end of WWII, the Haganah shifted their focus back to the British, waiting until British Foreign Secretary Ernest Bevin made clear he intended to take a pro-Arab policy, before joining into an operational pact with Irgun and Lehi. This pact was relatively controversial, but short-lived, falling apart due to Irgun's King David Hotel operation. Few major operations were carried out in coordination between the groups, and the Haganah agreed to cease operations for a time following the King David bombing, while Irgun and Lehi went their own ways. The Haganah's decision to attempt to incorporate Irgun (though not Lehi, who it eventually hunted down following Folke Bernadotte's killing) into the IDF was somewhat expected given Haganah's desire to win the civil war and avoid infighting, and it was also somewhat expected that given Haganah's dwarfing of Irgun's size (we're talking about 20x the number of members, roughly), that Irgun would be the one that was assimilated into the Haganah. Nevertheless, this was not smooth sailing, as demonstrated by the Altalena incident, where Haganah forces fired on an arms shipment brought in by ship by the Irgun. The battle, which was where the Haganah sought to determine its power over the Irgun once and for all, began with salvos between ships, and when the Altalena attempted to land on a beach near Tel Aviv, the Haganah opened fire on it. Menachem Begin, on the ship himself, pointedly told his soldiers not to fire back, saying Jews would not fight Jews. While the firing continued, and some Irgun soldiers may have ignored the order and fired back, and clashes spread. Eventually, Begin got on the radio and ordered Irgun to surrender and assimilate into the Haganah.

I say all this to demonstrate that the groups were not the same. It is debatable, even, whether or not the Haganah can be properly classified as a "terrorist" group under today's definition, while Irgun and Lehi were entirely willing to utilize methods we would call terrorism freely. We can't speculate largely on what level of support they got based on polling, because little to none exists. But based on recruitment, funding, and international legitimacy granted by discussions and endorsements from Jewish groups abroad, the Haganah was by far the most supported group, and the least prone to what we would call terrorism today. Indeed, one of their more infamous incidents was the Semiramis Hotel Bombing, an attack that led to Ben-Gurion sacking his own officials for their involvement in it for the death of civilians it reportedly caused, even though the Haganah had targeted it because they believed it was a weapons distribution center for Arab gangs. The bombing was incredibly controversial, including within Haganah, and it was during a civil war being fought against Arab irregulars, rather than part of a campaign against the British, who were getting ready to leave the Mandate behind (having announced their intention to do so since at least two months before the Semiramis bombing). As historian Benny Morris puts it, "The Haganah also contributed to the terrorist campaign, though its intended targets were what were believed to be Arab terrorist concentrations rather than civilians", which would generally mean it would not qualify as terrorism to begin with in modern terms. This distinction and the understanding of Jewish infighting is crucial to understanding why the Haganah emerged as the strongest group and the one whose leaders had unquestioned control of the state of Israel for nearly 30 years.