Who said they’d be singing kumbaya? I said they leave each other alone and don’t really care. That’s different than having a love-in between religions.
That said, though, it is quite common for one a church from one sect to help out another sect that’s in need. For example, when a Baptist church gets taken out by a tornado, it’s not surprising to see a Lutheran, Methodist, or Catholic church loaning them their facility so that they may hold services (Baptist services) for their displaced congregation. And vice versa.
That is happening TODAY in towns affected by the recent storms.