Why is racial segregation discriminatory, while sex segregation is a requirement and not discriminatory?

When women are not allowed into men's clubs, it's sexist. There have never been separate drinking fountains for women. It's just places where men and women undress that are separate, and that's because we have different bodies and there is a risk of sexual assault, right? Black and white segregation was living spaces, buses, shops - black people were not allowed into the white world at all because they were considered lesser. Places where women were not allowed into men's spaces were sexist, and that was fought against in the exact same way. Places where they're separated for physical reasons are because male and female have different bodies.

why should lesbians be allowed in women's spaces

Most simply, lesbians may have unwanted thoughts, but they don't pose as much of a danger. They are less likely to physically overpower, they are less able to sexually violate, and they cannot impregnate other women. In addition most lesbians understand that it's unpleasant to be leered at and will not want to seem threatening. Also, there are just a smaller percentage of lesbians among a group of women than hetero men among a group of men.

Nothing is a 100% solution, but changing with your own sex handles 99% of the problem. You can't really regulate "don't go in if you might do something bad", and where are you going to have lesbians change? But it's a small enough issue to just accept division by sex, although famously that has resulted in male bathrooms turning into gay sex spots in the past... I've never heard of the equivalent issue arising for women's areas though.