First things first, I searched the open internet high and low and couldn’t find much reliable source material, so unfortunately this answer took a deep dive into JSTOR and almost all the sources I used are paywalled. Not ideal, but it was the only way I could get a well-sourced answer.
I can’t give you an answer for Berlin specifically; but I can give you an idea for East and West Germany, whose LGBT scenes developed separately before the fall of the Berlin Wall in 1989 and reunification a year later. Then, since it’s much more recent, historically speaking, I only have a bit of information about post-reunification Germany. Surprisingly, there is a lot more literature documenting LGBT history in East Germany, so we’ll start there.
Sex between men was decriminalized in 1968. But, in the years leading up to decriminalization, arrests were rare and it was mainly the threat of potentially being arrested that kept folks out of the public eye.^(1) Of course, that doesn’t mean that queer people were accepted by their communities*.* It looks as though the road to acceptance began a couple of years later:
The domestic context in which gay men and lesbians shaped their identity changed significantly in the wake of the 1968 decriminalization and during the partial cultural relaxation under Erich Honecker after he assumed power in 1971.
Given the nature of governance, there wasn’t really much if any overt activism by East German gays and lesbians early on to speak of. Throughout the 70s, they quietly formed networks among themselves (much like the earliest years of LGBT organization in the United States) just to give themselves a place to belong. It wasn’t until the early 1980s in the cities of Leipzig and Berlin that “small circles of gays established themselves and very hesitantly articulated the interests of gay men and lesbian women.”^(2)
Once they started, however, they picked up steam and by the mid-80s, they were asking for things like open places to meet, representation in books and movies, and the ability to take out personal ads in papers.^(3) They were granted these things, which meant the ability to live their lives more or less openly beginning around 1985. After the fall of the Wall, the organization among these groups was thrown into disarray as activism was taken up by two national associations that spent an unfortunate amount of time arguing among themselves.^(4)
The gay and lesbian population didn’t lose the acceptance they’d gained through the 80s, though, so in the case of (now former) East Germany, the answer to your question is that the queer population began to really gain acceptance – first by the government proper and later through a combined governmental and social push for individualism – in the second half of the 1980s.
On the other side of the wall in West Germany, even before decriminalization, gay scenes began to re-form in most major cities: ^(5)
Hamburg's scene was the most developed, with twenty-four gay bars in 1959, two extensive red-light districts (St. Pauli and St. Georg) that provided areas of both male and female prostitution, and, in the first half of the 1950s, an impressive gay publishing industry that was responsible for some sixteen different titles. Frankfurt and Berlin's gay scenes trailed not far behind, with twenty-seven gay bars between them, several important associations and clubs for gay men, and their own small gay press for a period of time.12 Munich, Cologne, Stuttgart, and Hanover grew less developed scenes, which nevertheless included a few bars known for attracting a gay public.
Sex between men over the age of 21 was decriminalized in 1969 in West Germany. (Note: Both East and West Germany kept a law called Paragraph 175 after the war which was the source of the criminalization of queerness – the age limit here is related to that law, which still made sex with someone under 21 a crime due to the ‘corrupting’ influence of sex between men.^(6))
Homophobia was rife before 1969 and continued to be a strong social form of control even after decriminalization.^(7) As opposed to the quiet beginnings of the East German LGBT community, after the legal changes in the west of the country, there was a tide of protest and social activism going on. This activism came in waves that peaked in the early 70s and again in the early 80s. (Note: the source for this is discussing all social protest, not just LGBT, but the aforementioned are the general trends.)^(8)
The 70s were a time of tentative coming out for many LGBT people in West Germany. Rather than focusing exclusively on political activism, much of what took place was a more daily “I’m here, I’m queer” kind of activism that tried to gain acceptance from the wider community for those who identified as gay or lesbian. This led, in the early 1980s, to the founding of the nationwide gay/lesbian associations mentioned above.^(9)
These associations pushed for greater acceptance in both the political and social arenas and, much as in East Germany, over the course of the 80s. In the mid-1980s, the first openly gay and lesbian members of the Bundestag were elected, showing that there was at least some level of acceptance at that point. However, there were still some pretty big hurdles to overcome for the LGBT community to find themselves fully accepted by West German society, though they were at least tolerated by the late 80s.^(10)
Now with the separate trajectories of the East and West out of the way, we can look briefly at post-reunification Germany. In 1990, an advocacy group (Lesben- und Schwulenver-band in Deutschland) was formed that encompassed the entirety of the country which was able to put pressure on the government to expand the rights and protections afforded to sexual minorities. ^(11)
Among its successes was the repeal of the previously mentioned Paragraph 175 in 1994. They also argued successfully that disallowing gay men from the military violated their fundamental rights, though the law wasn’t changed until 2000.^(12) Everything else they’ve accomplished (which is a lot!) happened after the 1999 cutoff for this sub.
So, to conclude, the acceptance of LGBT people in East and West Germany was a slow upward trajectory from about the mid-1960s to the mid-1980s that seems to have sort of stalled at tolerance for the remainder of the decade. With reunification, the combined power of the entire country’s LGBT activism pushed past that into a more full acceptance of queer folks in Germany through the 1990s, both through political change and the resulting social pressures that come from that. ^(13)
And an end note here: My familiarity with LGBT history is mostly American and my knowledge of modern German history in general is pretty basic, so it's possible there are cultural nuances I missed in researching and writing this.
ETA: There's no mention of trans folks in this because I simply couldn't find any information about them. There's a dearth of transgender history pretty much across the board, unfortunately.
2, 3, 4. Gay and Lesbian Life in East German Society before and after 1989, Jürgen Lemke (1993)
*Styles of Masculinity in the West German Gay Scene, 1950-1965,*Clayton J Whisnant (2006)
LGBT Politics in Germany: Unification as a Catalyst for Change, Louise K. Davidson-Schmich (2017) (found here: https://www.researchgate.net/profile/Louise_Davidson-Schmich/publication/321381869_LGBT_Politics_in_Germany_Unification_as_a_Catalyst_for_Change/links/5a21ab520f7e9b71dd0341b0/LGBT-Politics-in-Germany-Unification-as-a-Catalyst-for-Change.pdf )
Sexuality in the Postwar West , Damar Herzog (2006)
The Dynamics of Protest Waves: West Germany, 1965 to 1989, Ruud Koopmans (1993)
9, 10, 11, 12, 13. Davidson-Schmich (2017)
Also, I didn’t actually use this source in writing this, but it’s an interesting read for anyone who has database access and wants to read it: Out of the Closet behind the Wall: Sexual Politics and Social Change in the GDR Raelynn J. Hillhouse (1990)
Piggybacking off of this, I'm curious about to what degree it really was all that accepted in the first place, and whether or not this is playing into a stereotype of a free Weimar Republic before the Nazis.