There are some women in trousers in the film. It is in crowd shots on the Academy steps.

You keep mentioning a brief romance between Uhura and Kirk and there has never been such a thing in TOS. The interracial kiss was not voluntary, aliens forced Kirk to kiss Uhura (and Spock to kiss Chapel) in "Plato's Stepchildren" by using telekinesis. Uhura had been friendly with Kirk in TOS but always very respectful and I doubt they would have ever kissed if the aliens hadn't made them.