From an earlier answer of mine

Ernst Röhm really was not an open homosexual in the 2018 meaning of the term; ie someone who openly admits to their sexual orientation. Instead, Röhm tended to be more candid about his proclivities in private NSDAP and other social circles, although he also tried to compartmentalize his personal life away from his political one. His autobiography likewise tangentially attacked Paragraph 175, the statute of the German criminal code against sodomy. He would attack German prudery and hypocrisy that prevented men from acting on their passions, a coded attack on 175. Röhm's activities sometimes landed him in an occasional police questioning, especially since the NSDAP's political rivals sniffed out an obvious scandal. The SA leader would never deny he was attracted to both men and women in these interrogations, but he always denied he had actually broken Paragraph 175.

Some conservative commentators both in the early FRG and in the post-Cold War US have taken Röhm's sexual orientation as an example of Nazi depravity and how at ease the Nazis were with homosexuality. This is an untenable thesis as Röhm was something of an outlier in the Party in terms of his personal life and indiscretions. Moreover, his homosexuality was a component of a larger matrix of how he conceived of masculinity's place in the new order.

The SA leader cultivated a very hypermasculine image both in his own life and his leadership of the SA. According to Röhm, masculinity was the highest form of power and discipline. He valorized the camaraderie of the frontline trenches and male community. Röhm's Weltanschauung associated chaos and disorder with feminine characteristics. His ideal world was one in which women had little to no say and male virtues reigned supreme in society. His attacks on Paragraph 175 obliquely as a public figure were notable, but he was no Magnus Hirschfeld; Röhm's views on sex almost exclusively focused on male pleasure. Lesbianism or even straight female sexuality had little space in this vision of an ideal society. He in private maintained that his sexual proclivities were just an expression of this masculinity. But gay liberation was not his main focus. Rather, Röhm framed male same-sex sexuality as a component of a social order that was highly patriarchal and very heteronormative when it came to defining masculinity. The ideal men in Röhm's view were to be militaristic and men of action. There was little room for alternative masculinities such as crossdressing in this narrow definition of gender.

It was this regimented, violent, and predatory masculinity that made Röhm an asset to the NSDAP in its seizure of power. This is not to say that Röhm's sexuality was not a liability in the NSDAP's rise to power. An SPD newspaper, the Munchener Post, published a widely-read expose of Röhm in 1931 and claimed the NSDAP's Brown House was a den of homosexuality. Other enemies of the NSDAP would also allude to the homosexuality of the highly homosocial SA and Hitler's entourage. Yet the problem was that the political parties that would attack the NSDAP on these grounds tended to be those who had earlier attacked Weimar's restrictions against homosexuals. The SPD, for example, had been one of three parties who had proposed ending Paragraph 175. The homosexual charge did not gain much traction within the socially conservative political parties of the German right, many of whom were hemorrhaging voters to the insurgent NSDAP and whose leadership were in the process of seeking an accommodation with Hitler. As for the NSDAP itself there were some decidedly homophobic elements within the party, especially Alfred Rosenberg. But the party's leadership tended to twist Karl Lueger's infamous dictum "I decide who is a Jew," with regards to men like Röhm. While both Goebbels and Rosenberg were willing to excoriate men like Hirschfeld as alleged exemplars of Judeo-Bolshevik perversion, Nazi propagandists hypocritically ignored homosexuality among its own ranks just as they ignored the other social weaknesses of its leadership such as Göring's drug addiction. So it was not his ideas on sexuality that brought Röhm and the SA down. Röhm's ideas on social leveling via mass paramilitarism made him powerful enemies within the Reichswehr. Additionally, the SS also recognized that Röhm was a rival, as did Göring. Both the SS and Göring began to conspire together to bring the SA and its leaders down and Röhm's sexual proclivities were a preexisting weapon to use against him. This constellation of enemies meant that Röhm's star fell precipitously after the initial seizure of power. His homosexual activities became a liability in this internal power struggle, but they were just a pretext for the extrajudicial murder of the SA's leadership during the Night of the Long Knives.

Sources

Hancock, Eleanor. Ernst Röhm: Hitler's SA Chief of Staff. Basingstoke: Palgrave Macmillan, 2012.

Siemens, Daniel. Stormtroopers: A New History of Hitler's Brownshirts. New Haven: Yale University Press, 2017.