In an accepting world I think the furry fandom would still be quite large. The accepting community is why a lot of people stick around, but there are many other reasons for it to exist which aren't influenced by being persecuted. Some people feel like they're inherently furry from birth, like a gay person would, and some pick it up during their life as something they want to be associated with aesthetically or otherwise. You've also got therians and various other subcultures that are heavily based around the furry/animalistic themes themselves without considering any sort of societal values.

I also personally think pseudo-anonymity is healthy even when all of society is accepting, and I suspect there's a large draw in being to socialize and try out different versions of yourself while keeping the option to burn your account and start again if you make mistakes. Now more than ever in our surveillance state, it's nice to leave your identity behind and say things without worrying about it coming back to you IRL. I personally find furry/animal avatars to be a fun way of achieving this without needing to pick something boring and impersonal.

As for gender disparity I don't think this is any inherent aspect of the furry fandom but just how predominantly-online cultures are weighted in general. I'd expect this to change given enough time. You can see recent gender studies here, and I highly recommend checking out some of the other pages from their findings if you're interested in some of the bizarre trends that furries have compared to the average person. I wouldn't be surprised to find out that being furry is heavily biased by specific genetic circumstances, and that the explosion of furry culture is a figurative opening of Pandora's box.

Edit: Also I found this page and the graphs+text have a lot of overlap with this topic.