Well, he'd only know about how you voted if you got into a converstation involving politics or he / staff looked at the political bumper stickers on your car.
Somehow I didn't have any trouble with the doctors I saw in MA who had all sorts of material posted in favor of Clinton's plan in the early 1990s.
I think there's a difference between "I like this PLAN" and "anyone that voted for that guy, go away."
I would expect doctors to have a political view on anything involving healthcare. That's part of their job, it's the middle of their lives, etc. A doctor having and posting a view on healthcare, or a specific healthcare plan, isn't the issue here.
It's a doc saying if you voted for a specific candidate, you are NOT WELCOME. And that really looks pretty close, to me, to saying if you're black/Jewish/Asian/purple/whatnot, don't come here.