Should Christians purchase dinners from denominational churches?
Start by reading Should a Christian attend a university operated by a denomination? It covers many of the basic principles we need to discuss.
The core question is: Does the purchase show support for the denomination and its teachings? For example, in a number of places, the Roman Catholic Church holds fish fries to raise money. If you purchase food there and ate there, it would be reasonable to assume that you support the teachings of the Catholic Church. Let's just suppose that the local Baptist group had a booth at the county fair and sold ice cream cones. It might be argued that you are just purchasing a product that just happened to be sold by a denomination, but you still need to consider if others around you would view it the same way.
One way to test the purchase: What if an LGTB+ group or an Abortion Rights group was selling the same food? Would you still purchase it because you are confident that doing so would not support the group's cause and it would not cause others to think that you agree with their agenda? If you would not do the same thing with a group you adamantly disagree with then it would be best not to associate yourself with a denomination selling the same thing.