should someone be punished for their views?

That seems to be the direction society is going. It's completely unAmerican, but that's the way it's going.

If their views are that people unlike them don't deserve civil rights and other privileges they themselves have, then yes, those view cannot be tolerated. I'm fine with those individuals losing their jobs or scholarships, being kicked off teams, having landlords refuse to renew leases, etc.

I would not be okay with them being physically harmed for hateful views.

No they shouldn't................

I do not think so.

Well....  If the view of my neighbor's yard is unappealing, because it's got trash and junk everywhere, then yes, perhaps the city should punish him with a citation and hefty fine.

But...  if someone just has an opinion about something then no. 

Yes, If they affect other people races, genders, and sexual orientation.