There's a difference between supporting sin and supporting a business run by sinners. If you refused to do the latter you'd have to go live off the grid in the woods and raise your own food, because everyone, whether they operate their own business or not, sins. Boycott the gay-owned sandwich shop, and your alternatives are the sandwich shop owned by the guy living with his girlfriend, or the shawarma stand owned by Muslims.
It's no wonder that when St. Paul reminded the Corinthian church not to associate with sexually immoral people, he immediately qualified that by saying he didn't mean people in the world, because you would have to leave the world entirely to avoid them (1 Cor. 5:9-10). In a pagan society, doing business with pagans is a practical necessity.
Chris said he didn't know what the politics of the shop owners were, so I infer that there is nothing in the shop openly promoting gay causes. So by buying lunch there, arguably you are not supporting homosexuality, you are purchasing goods and services. Which is different from a corporation that targets gays in their marketing: in that case, a portion of your money is going to promote immorality, and I'd say a boycott was arguably justified.
I do not think you read, or if you did, understood my post. Either way, I stand by what I wrote. Franklin Graham is correct. The Christian Churches are being attacked by the LGBT community. The laws that are being passed are intended to persecute Christians. If you cannot understand that, my explaining further will not enlighten you. I and many others stand with God, truly stand with God. God gave you free will to choose what side you are on. You have made your decision, so have I.
Yeah, if they started promoting items from the gay agenda within the store, then I would have a problem going there.
Doing that would make me feel like I am not welcome there to be honest.