To the contrary, would it be okay then, to wear a religiously symbolic pin (Cross, Star of David, Star and Crescent)? If the answer is no, then the answer might be the same for a Pride pin.
Can't see why that'd be inappropriate, so long as it was normal small lapel-pin size. Plenty of people wear crosses or star of david necklaces, or yarmulkes, or hijabs. Hell, some people set off *everyone's* gaydar (even if they aren't gay). There are also plenty of names which are heavily associated with certain religions or ethnicities or whatever attribute someone could find a way to take offense to.
And a pride pin is not broadcasting your sexuality. Many people wear them who are not LGBT themselves. It's a gesture of acceptance.
I was led to believe that physicians should appear to be non-biased. Wearing one thing or the other indicates that they favor a particular ideology, thus alienating someone else. Regardless of what the majority of people believe or think, no amount of patients should be alienated or made uncomfortable.
This is why I would support not wearing anything that could indicate bias (even though it is morally justifiable to support a cause), I feel that it is inappropriate.
I am not going to be the right physician for every single patient. That's OK. Some people won't want a white physician, or a female one, or a young/old one, or a [insert stereotype people make about me from appearances with no symbols displayed] one. I would rather a group which historically has had difficulties discussing this topic *which can directly impact their health* know that they have a provider that they can trust, than worry about the small number of people who are vehement enough about disliking LGBT people that they will avoid a physician who shows the smallest sign of supporting that group. Why? That population has a much larger pool of other physicians they can turn to. If they don't like me, well, there are 10 people next door who are me without that pride pin. The converse is not necessarily true, as physicians with pride pins are far less common than those without.
If creating a safe space for minority/oppressed groups is inappropriate, then oughtn't we eliminate all specialty clinics, like Pride clinic, Hispanic clinic, etc? Religious affiliations can make some people uncomfortable...should we rebrand all religiously based hospitals (Lutheran, Mt Sinai, etc) and make sure not to hang up diplomas from schools such as Loma Linda or Yeshiva or Temple? Is it OK for physicians with traditional families to have a (small, tasteful) photo of their spouse/children in their office? Doesn't that also advertise their sexuality? What if their spouse were the same gender as them, or a different race? Some patients might be uncomfortable with that. Where is the line?
Physicians are also people. Being a person is not unprofessional; being a bigot is. There is a difference between allowing signs of who you are under the white coat, and letting that impact how you treat your patients, and
that is the line to be concerned about.