(As a personal preference, I'd rather not know the political views, legitimate or otherwise, of people I work with. It's not relevant.)
As to your first - if people with a strong set of ethical and moral principles "just shut up" about what they considered ethical and moral essentials ... then they wouldn't be who they are. The only people who don't show what they hold good are people who don't hold as good much of anything.
Now if we're just talking "opinions" here (about things that are not ethical and moral, merely matters of taste), then yes, a person with "strong beliefs strongly held as a universal principle" is someone who is just an ass. But if I know someone is a raving Detroit Lions fan "on the internet", what kind of a person am I if I can't work with them?
I have only ever seen CoC's abused to push out people with anti-social just views.