I don't think gender has any bearing on how one performs their job and to promote such a thing could do more harm than good.
When I see someone with their pronouns on twitter I usually don't engage with them. People who do this more often than not tend to make everything about gender politics where it would otherwise be irrelevant.
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.
Not to put too fine a point on it, but what gives you the right to tell other people what's important to them, given the vastly different set of life experiences everyone has?
Maybe if someone was throwing their life away to addiction, but an otherwise functioning and happy person doesn't seem like someone who wants to hear what you think of their life, and would seemingly prefer to just be called by the identifier they've chosen and then otherwise left alone by you.