It's important for healthcare safety that people feels safe to discuss their gender and pronoun badges are a small sign that the wearer is a safe person to speak to.
Yes, that's the point. When Bob goes for treatment and everyone assumes he's cis-male but he's actually trans-male they may offer needless screening. Bob needs to feel safe to be able to say "I've never had a prostate".
It's important for healthcare safety that people feels safe to discuss their gender and pronoun badges are a small sign that the wearer is a safe person to speak to.