Well, duh.
(Believe me, I really didn’t want to say “duh”, but the shoe fits.)
Jewish people don’t try to fool people into thinking they are Christians.
“There are also probably other “Christian” denominations”
.... Yeah, they’re called heretics, cults, apostates, etc.
Depends on whose shoes you're wearing. The fanatical among them would probably say the same about you. I'd say such people were just born 500 years or so too late.