Absolutely has the power to do so. He was voted in by the public to run the city and do his best for public interest and to keep it safe and discrimination free. It is in public intrest to squash discrimination. I feel he is doing his city a service by saying he will not allow a company that is so openly discriminatory to do buisnes. Its the same as keeping a proper police and fire protection imho. If the folks that live there don't agree with his actions they can vote him out at the end of his term.
As for me I won't be providing Chic Filet any more of my money. Not that i ate there often but i will spread the word to my friends and family.