EXACTLY my feelings! We all (allegedly) believe in the God of Jacob and His Son. Of the differences, they are entirely earthly. When we die, God will sort us out. Using Him as a political tool is the height of sacrilege.
My aunt was a devout Baptist who married a devout Catholic and it worked for them. Sometimes they went to his church and sometimes they went to hers. Other times they went to their own churches by themselves. They always went to Christmas mass at his church.
I don’t know how common it is but the Methodist church of my youth always had a midnight Christmas mass.