Actually, I understand his father’s mother was not Jewish, which is why he was basically kicked out of the Marx family and was unable to train as a Rabbi.
She had attempted to convert, but Marx (the dad) was a Cohen (their actual name was “Levi”) and thus not eligible to marry a convert, so he left Judaism altogether. It had nothing to do with employment.
Marx’s mom was of some sort of mixed heritage; I would have to ask my wife -— she is actually kin to this crew (along with Adm. Hyman Rickover, which is ironic as heck), which is the only reason I know this.
Marx’s mother was Henrietta Pressburg, a child of Dutch rabbis with Czech origins.
http://www.uv.es/EBRIT/macro/macro_5004_0_0.html