I may have stumbled upon/duh-ed my way into a gender privilege situation with my post on exercisewear. Generally speaking, at the gym, female-presenting people are more likely to wear coordinated outfits, while male-presenting people are more likely to wear Umbros and muscle shirts. The disparity tells us something about the messages each group receives.
I feel a desire to dress up most days. Now imagine a feeling like that but an order of magnitude more intense and overbearing--more a mandate than a desire--which drives women to dress up for the gym (and pretty much everywhere else to boot) and leads men to think, "What? Why are they doing that?" because men are not expected to dress up for the gym. The idea is called femininity as performance (link may be NSFW depending on your employer) in social justice settings.
So wear whatever you want to the gym and, in keeping with the Dapper District Social Justice Committee's strictures, refrain from judging anyone, of any gender, race, religion, ethnicity, etc, for what they wear.