If you don't mind, I'd be interested in hearing more of your views about sexism in Star Wars. A lot of women see Leia as a feminist icon. The most sexist thing I noticed in the first two movies is Han Solo's attitude towards Leia, although he's kind of held up as an object of ridicule. He's sort of portrayed as a cocky braggart who isn't as badass as he thinks he is. ROTJ has more problems, though. The new movies aren't sexist at all and actually have a lot of alt-right types pissed off. I read one article that suggested alt-right trolls created bots to downvote the latest movie on Rotten Tomatoes because it promoted an "SJW agenda."
I don't know that Star Trek, from what I know of it, has an especially great track record on sexism until DS9. But, I'm open to my view being changed.
It's been awhile since I have seen any Star Wars, and I have seen only the original three, plus the first one made after that. Yes, there is Leia in the first 3, but she is the token "female who gets to do anything interesting". Compare with how many significant male roles there are. Presumably the societies in both SW and ST are about 50/50 male/female, which makes this ratio improbable absent any credible explanation. Then there is the fact that Jedi are only men. This is likewise never explained, just assumed. Things get a bit better when they introduce Padme and her entourage, but still, the ratio of significant male to female characters is quite high, and the big focus on Padme seems to be her relationship with a man (Anakin), and not what she is trying to do in the senate, or for her home planet.
Star Trek is almost a generation older, so one would expect even more sexism (and racism), and there certainly was some. The forced choice between Spock and Number One after the series pilot was because a woman first officer was seen as a risky venture, as risky as a recurring alien in a responsible role. Producers were unwilling to take both risks. Majel Barrett was therefore moved to the more stereotypical role of a nurse and Spock became "number one". Still, the ratio of significant female characters to male was much higher than in SW, even in the original series. There were three in the regular crew: Uhura, Nurse Chapel, Yeoman Rand. Though their positions were rather traditional, their role in the plots did not focus on relationships, but rather on their contributions to the action. A large number of the "guest" characters were also female, including ambassadors, nobility, entertainers, ship commanders, and scientists.
So, on balance, ST always seemed to me to be pushing the envelope on gender balance much more than SW. I understand SW is finally catching up with its first female Jedi. I am curious as to whether they explain this development in the context of the story. It is also a bit disturbing that it is this first female Jedi who I understand is finally allowed to go beyond the traditional Jedi stoicism of detaching from emotions and keeping relationships at a distance. That is probably more healthy, but stereotypical as presented.