It's not your call whether someone feels they need to wear a cross to be Christian, or a rainbow to reflect their beliefs on that front. YOU may think someone is missing the point if they must wear a cross to be Christian, or a yarmulke to be Jewish, but your personal opinion on that front is, frankly, irrelevant, and shouldn't dictate their own personal expression of their beliefs.
Sidenote, even if you're wearing a rainbow to be queer (and there are multiple other reasons you would do such a thing other than being gay yourself)...that doesn't automatically make it political. The existence of gay people is not a political debate, it's a fact. Being gay is not a political statement. Relevant political debates include things like same sex marriage, etc., but the mere acknowledgement of LGBT people is not a controversy.
I will treat every one of my patients. If they choose to go to a different physician because they don't like something about me, that is their right and their decision. My responsibility is not to treat someone differently because they disagree with me. It's not to erase any trace of personality or identity that they might not prefer or agree with. That's not even possible, and I'm not sure it's a desirable goal to begin with.