Ancient acceptance of MSM generally depended on who did the penetrating, because in a nutshell penetrating was manly and A-OK while being penetrated (orally / anally / vaginally) was womanly and hence bad. MSM was an exercise of social power.
The "trans/gay/lesbian is cool now" explanation doesn't hold a lot of water to me. If I had the choice to not be gay, I wouldn't be. Life would be so much easier, emotionally and otherwise. Sex would be lower risk and it would be much easier to find a romantic partner. I spent a long time - two decades - suppressing it, as hard as I could, and it did not go away. Instead I was anxious and depressed. After I started to accept myself, those things became a lot better. I look forward to the day I come out.
Transitioning is 100x harder. The nonconformity is obvious. The antagonism directed at transitioning people is unavoidable, strong and potentially deadly - violent and lethal attacks on trans people are becoming much more common every year. Compulsory sterilization for people legally transitioning is still mandated in many countries and was only abolished in progressive countries in the last few years.
No, nobody is doing any of this because it's "cool".
Yes. Outright bans and persecution of homosexuality is relatively new. Effeminate gays were practically eradicated, Europe had the Nazis do it, the US had the lavender scare (because gay=communist), the Soviets under Stalin did much like the Nazis. This is why gays reinvented themselves into the hypermasculine leather culture starting in the 50s. It's why older gay men have negative attitudes towards younger effeminate gays and the reason why the same parts of the gay community look down on bottoms who aren't vers.