I'm a MAGA guy, go to Church and barbecues, but unless it is a Church sponsored event, I've never seen people singing "Church songs" at a cook out.
At a Church event, no one eats until the Priest gives a Blessing and we all recite a prayer.
If it's a volunteer fire hall event {yep, we still have volunteer firemen err, fire persons}:) there is generally no formal prayer {unless a person of the cloth is present}.
I attended a volunteer fire department fair in Mineral, VA on Saturday, and it was wonderful. Corndogs on a stick, fattening food, a few carnival rides for the kids, and some games to raise money.
Small town USA in southern Virginia, and there were people of all colors and lot's of local cops.
Everyone was having a good time.
If you go to a neighborhood cook out, it depends if a prayer is said and if later in the evening, some one sings, it's because they have had a few too many, and generally it's not Church songs.
If you’re going to bbqs where a “priest” says a blessing, then of course you haven’t had this experience. It’s an “evangelical” thing, and country.