Not it doesn't. It's basically the exact same filet and prep (pickle brine), same size, manages to be blander than a regular CFA spicy chicken sandwich, and is twice the cost of a deluxe spicy CFA sandwich. It's a ridiculous sandwich. I've had to try the Chicken Shack a second time to confirm this for myself, at a different restaurant, because I didn't believe that it could possibly be as mediocre as it was the first time I tried it, but it is. ...not to say it is bad on its own, but I could have two superior CFA deluxe spicies for the cost of one plain Chicken Shack.
As for the boycotts, it isn't about them being Christian, it's about the longstanding homophobic policies of the Caffey family. They have a secondary charity foundation that has long donated a lot of money to anti-LGBT groups like Focus on the Family and, I think, for a time were sponsoring some of those radical missions in Uganda (the same groups that were actually helping Ugandan nutsos to execute gay Ugandans, but largely supported the Ugandan federal banning of homosexuality). There were two such boycotts that I recall, and in both the Caffey's promised to de-fund/separate from these controversial groups. Obviously that didn't happen the first time; not sure about the 2nd (the one that prompted "Freedom Chicken!" and sociopaths like spidey posting their "daily loadout" pics all over the internet of pistols, knives, and chick fil-a sandwiches, lol.)
Boycotts absolutely do work, but few such successful boycotts have ever had to contend with the deliciousness of CFA sandwiches.