As I see it, Cady and his restaurant chain are being persecuted for making public statements which were based upon the Bible's teachings that call homosexuality an abomination to God (Lev. 18:22; Rom. 1:27). According to the U.S. Constitution, Cady has every right to believe as he does, and every right to state his views publicly. However, while he has the right, was it prudent for him to do so? Jesus said, "Behold, I send you forth as sheep in the midst of wolves: be ye therefore wise as serpents, and harmless as doves" (Mt. 10:16). Having the right to do something does not mean one will not suffer the consequences.
Just as Cady has his rights protected by the Constitution, so do those responding in protest. They may demonstrate, picket, boycott, or whatever, as long as they act within the law. However, why is it okay for supporters of gay rights to demonstrate freely, but Christians are repeatedly thwarted from doing so at abortion mills? Why do Christians need permits, and why are they required to stay a specified distance from the entrance of the "clinics?" And, why is it that the liberal politicians jump at the opportunity to support their picketing, but conservatives hesitate to do so for anti-abortion groups?
I commend Cady and Chick-fil-A for publicly standing for the teachings of Scripture, and I certainly hope all those who agree with his statements will do their part by frequenting his restaurant chain. I hope his supporters will also take note of those politicians' stance and remember it on election day. I also hope law enforcement will treat all demonstrations, liberal or conservative, equally.
Jesus also said, before you take a stand for Him, you'd better count the cost (Lk. 14:28).