Blocking construction of Chik-fil-a restaurants over Cathy's views is a violation of Cathy's First Amendment rights. Boston and Chicago have no more right to stop construction of Chik-fil-As based on an executive's anti-gay views than New York City would have had the right to block construction of an Islamic community center blocks away from Ground Zero. The government blocking a business from opening based on the owner's political views is a clear threat to everyone's freedom of speech—being unpopular doesn't mean you don't have rights. It's only by protecting the rights of those with whose views we find odius that we can hope to secure them for ourselves.Yup. I'm not going to go out of my way to boycott Chick-Fil-A, because I've never actually had a meal there that I recall. But that's my private choice. A government decision to punish somebody's political or religious beliefs is wrong.
More to the point, it may also get in the way of actually advancing gay rights. One of the counterarguments to gay marriage is that conservative Christians fear they'll be legally required to, essentially, bless such unions. They see rights as a zero-sum affair: If gays win, they lose. That's not the way it has to be, and it's not the way it should be. If Boston and Chicago mayors prove otherwise, that will stiffen religious resistance to civil marriage. Which means that those cities' mayors aren't just wrong, they're also being tactically stupid in the service of scoring political points. That's not really all that principled.
UPDATE: A friend says that the mayors aren't actually threatening to block construction. That's mostly true: Boston's mayor started out in that spot, but backed off. Chicago's mayor is apparently just being blustery, but an alderman there seems to be trying to block stuff nonetheless. I don't blame these men for articulating their values, but government officials should always be leery of being seen as using their official powers to chill speech.