We absolutely should use the pronouns and names of people as the gender they identify with, BUT whenever something is separated by gender, we need to consider WHY it is separated. For the most part, we should be treating the genders the same regardless, so in most cases, it doesn't matter.
Sports is separated because we believe that biology confers advantages. Otherwise there would be no need/desire to separate sports by gender.
Lockers are separated because its a place where people people need to shower and change clothes, which involves being naked and have a reasonable expectation that they won't encounter exposed genitals of the opposite sex.
Bathrooms have privacy stalls. The reason bathrooms are separately gendered is primarily social.