See, I can see goes this will go. Some well-mesning, or woke misogynist, team leader will turn up on shift with the bag of badges and say "we all need to wear these to show our support to the LGBT community. Most people will comply (because work, boss, ignorance, etc). Team leader gets to record their film team's compliance.
Then that doctor or nurse goes back to work, and then sees female patients who clock the badge and immediately feel uncomfortable because what that badge says to her is that women's consent and boundaries do not matter to this HCP.