How would liberals react to such a stand by a mayor of a conservative minded city? There would be riots and boycotts and demands for impeachment and election do-overs within moments of such an outrage of a government official acting out against a private business.

YET! This is real;
Boston Mayor Thomas M. Menino also blasted Chick-Fil-A for its stance, and vowed to block a proposed location near the Freedom Trail, a popular Boston tourist spot.....
......He said getting licenses to open in the city “will be very difficult – unless they open up their policies.”

Should politicians really be able to choose which descriminatory stands private businesses take for social issues by making it "difficult" for businesses that don't agree with their social standards to conduct business in "public", United States of America, land of the free..... areas?

More leftist divisions of Americans. If homosexuals don't want to buy Chik-Fil-A, they have the right not to do so. Shouldn't the citizens of Boston have the right to decide whether they personally want to support a business rather than have an elected official dictate to them what will be available to them?