Transness probably has more of a biological root compared to the therian phenomenon, but there are obviously sociological factors as well. It's like how some people think if we abolished sex as a social class then people wouldn't feel dysphoric. A lot would probably still want to change their body, but yeah it's fair to say they'd likely have less dysphoria at least. Eg, there's a difference between a face feminized be estrogen and one masculinized by testosterone, but then there's also cultural ideas of masculinity and femininity related to facial hair and makeup. I'd imagine in such a society you'd have people going on hormones but having a lot less anxiety about passing.

The issue is we don't fully understand the brain and we can't make societies in a jar. So all we're left with is attempts at reasoning.