I definitely care if my doctor is some anti-abortion, patriarchal Christian who votes Conservative, but I hardly doubt wearing a cross or not would indicate their inability to fulfill their role as a physician because of those values.
Either way, a political criticism of genocide is not the same thing as a general religious symbol, so there's no consistency between these cases in the first place. Everything your doctor subscribes to is rooted in their politics, and a watermelon pin that shows solidarity with a nation currently victimized by genocide is like, a pretty bad starting point for this enforcement against political expression.