No, having separate bathrooms is not sexist. Because the term sexism refers to negative issues only. Webster's uses the word "discrimination". Which I assume you are being pedantic and interpreting in a broader context like "discriminating between the colors blue and teal".
But lookup discriminate and it has a few meanings. One of which refers to prejudicial or unfair treatment. That is the definition implied when referring sexist discrimination.
But lookup discriminate and it has a few meanings. One of which refers to prejudicial or unfair treatment. That is the definition implied when referring sexist discrimination.