While I was living in Oakland, there was a particularly ugly racist group and criminal organization with a front called "Your Black Muslim Bakery" (perhaps you've heard of them). They had a long an notorious history of extortion, rapes, kidnapping, and torture, but not only were they left alone by the authorities- they actually enjoyed the patronage of local politicians! They weren't shut down until their leader ordered a hit on Chauncey Bailey
WP, a prominent journalist who was gunned down in downtown Oakland in broad daylight.
It's off topic to talk about Chik Fil A, but I'd say that no, they should not be shut down by force because of the political beliefs of the owner. They offer the same service to everyone, so it's not a valid analogy to compare them to an openly racist company. If you don't want them to have your business, then don't eat there.