Green’s Dictionary of Slang

come-to-Jesus adj.

[1920s–30s] (orig. US tramp) insincerely pious.

In compounds

come-to-Jesus coat (n.) [as worn by, inter alia, ministers and preachers]

[1930s–40s] (US) a frock coat.

come-to-Jesus collar (n.) [the preference for such collars among revivalist preachers]

[1920s–40s] (Can./US) a stiff dress collar.