In the revolver days (before semi-auto pistols) a church gun was a normal firearm as described above. After the semi-auto pistols arrived on scene this term applied to mostly Colt 1911's. Current times this can apply to any firearm that has custom work designed to enhance mainly appearance and, much of the time - functionality.
However, this should not be confused with a (today's term) "bling gun" - which can imply that the gun is more for show than effectiveness. Or that the user is not proficient in its use because it is only worn on special occasions.
In the Southwest BBQ's could be at a casual get together, a special event, wedding, or a different/very formal affair.
Also known as a "Church gun," a "Court Gun," or "the 4th of July gun" (in Wyoming) for obvious reasons.
"He's wearing his Sunday best and his BBQ gun."
"The Sheriff showed up to court wearing his BBQ gun."
Uh-oh, here's Mike with his BBQ gun again. Everyone act impressed.