I'll direct this answer to the question about Rohm specifically:

Rohm wasn't the leader of the SS, he was leader of the SA; a different organization although around the time of Rohm's leadership the SA was nominally in charge of the SS.

Now there are different reasons as to why different officials were accepting of Rohm

1. Rohm was a decorated frontline soldier in World War 1, who had then played an active role in defeating the Communist revolution in Bavaria and was committed to the same ideological goals as other Nazis. For people like Himmler, Rohm's personal bravery and accomplishments superseded his homosexuality at first.

2. Rohm was incredibly powerful. he had personal control of a large arsenal of weapons after the militia he organized during the Communist revolution was disbanded and a network of friends and allies within right-wing circles. Rohm was able to create a force of 10,000 SA members, which grew to 30,000 when Hitler left prison, 500,000 when the NSDAP had grown in popularity, and 4,500,000 when Hitler assassinated him. That's a lot of men he commands, and that he can give to Hitler.

3. Rohm was personally very able. When Rohm left the SA it collapsed into infighting and turmoil, Hitler had Rohm brought back specifically because he was a strict disciplinarian and good organizer, and Rohm promptly whipped the SA back into line.

Now Rohm still dealt with homophobia. Hindenberg refused to shake his hand and many senior figures were openly antagonistic towards him. Rohm's homosexuality also seemed to bother Hitler, when Rohm was arrested at a spa he was in bed with a young man and "came close to being shot on the spot by a furious Hitler." this is unusual because Hitler had been incredibly nervous prior to this, and actually wanted to let Rohm live later when he was imprisoned and had to be talked into actually killing Rohm by Goring and Himmler.

Hitler also overlooked the homosexuality of General Werner von Fritsch in 1936 and ordered Himmler to destroy a file of the SS' investigation into this when Himmler confronted him. This seems to have been driven again by usefulness, Fritsch was the supreme commander of the army and was a key figure in expanding it. When von Fritsch began to protest against Hitler's plans of expansion Hitler reopened the case (although it was later proven that General von Fritsch wasn't actually homosexual and had been confused for Captain von Fritsch who was)

Now, none of this really explains their friendship which did exist - Hitler's support was the only reason why Rohm was in power for so long despite antagonizing everyone else, and Rohm addressed Hitler as a personal friend rather than as his boss. As with von Fritsch however, I think the answer was just that Hitler could tolerate homosexual people as long as they were useful to him since we know that it did bother him but he was willing to overlook it even when he wasn't friends with the person in question.

Source: Adrian Weale - The SS: A New history

You can look at this question individually or systemically. In other words, how could Roehm and Hitler be friends as individuals, versus how did male homosexuals generally fit into the Nazi movement?

Woodstovia covered the first one well in their comment -- Roehm was a capable soldier and logistician for the cause, and the Nazis needed him. Hitler needed him. Roehm was actually a bigger deal than Hitler when they were starting out in Bavaria in the early 20s, and even as the movement grew Roehm retained his own source of independent authority as the leader of the SA militia. According to a many sources, the two got along well together and even used the informal "du" address, which Hitler only allowed few people to use. From my reading of the sources, they actually liked each other. But then of course any personal friendship they may have had didn't stop Hitler in the slightest when murdering Roehm became politically convenient.

And so that turns us to the other way of viewing this, as the larger situation for male homosexuals in the Nazi movement. There was indeed a certain stereotype of homosexual men in elite military positions. In some ways this could go back to Frederick the Great (Prussian warrior-philosopher-king who lived among men and cultivated good looking soldiers), and in the immediate case to the Eulenberg affair that OP mentions. Around the time of that affiar, authors like Adolf Brand and Hans Blueher published philosophical works glorifying male homosexuality among soldiers and political leaders as the highest form of civilization. They (especially Blueher) scorned femininity, which they connected to weakness and pacifism, and wanted to live in an all-male community of fellow fighters in contrast to public images of gays that they found effeminate and degenerate. You can see the appeal of the Nazi movement to them -- all about fighting and masculine posturing against supposed social weakness, while creating an all-male living environment with the militia. They were never large in number though, most stormtroopers of course were straight, but they did have a man at the top to legitimize their presence.

So why did Hitler have Roehm and his circle killed? He no longer needed them. They were street fighters, disruptors, chaos makers who played a role in undermining public order, and therefore confidence in democratic order. The Nazis loved to start riots and street violence, then ask "why can't the republic control the streets? Elect us and we will bring order." So once they took power, their incentives flipped and the SA was now a liability rather than an asset. They scared the Army, because they were a huge, armed militia. They scared the industrialists, because they represented the economic complaints. In decapitating the SA, Hitler demonstrated that the elites could continue as usual as he dissolved leftist groups, persecuted the Jews, and planned for war.

Hitler didn't have Roehm killed because he was gay, but once he did kill him that was his excuse. In his famous speech after the Night of the Long Knives, he told the nation that he had discovered a homosexual plot among Nazi ranks, had acted to purge it, and now every mother can trust giving her son to the Party without him getting molested. I'm paraphrasing obviously, but that was the main story. (The other strain of the speech was Roehm's supposed socialist plot against Hitler, which was entirely invented.)

In the end, Klaus Mann's prediction that gay Nazis "tied their own hangman's noose" proved true. They only had a place so long as they were useful as fighters during the drive to power, and as soon as they weren't they were killed or expelled. In Roehm, we get the personal and the structural combined in one case study.

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Sources -- each of these are great full length books:

Eleanor Hancock, "Ernst Roehm" (2008) - a biography, the first in English in Roehm, fully incorporates his sexuality

Laurie Marhoefer, "Sex and the Weimar Republic" (2015) - more about sexuality than Roehm himself

Daniel Siemens, "Stormtroopers: A New History of Hitler's Brownshirts" (2017) - current definitive history of the SA overall

Andrew Wackerfuss, "Stormtrooper Families: Homosexuality and Community in the Early Nazi Movement" (2015) - specialist work on exactly this question and similar ones