"My Daughter tells me you’re half-Jewish" "Just my good half"

I’m sure most people have encountered this sort of trope. The quote I used is from Goodfellas, but it appears in a lot of films, particularly in this era. The character is about to meet his Jewish girlfriend’s mother, but the character isn’t Jewish, so she goes “well we’ll just say you’re half”. But my question is, does this ring true? For people with mothers religious enough to be bothered that your spouse is Jewish, why would having a Jewish father factor into it, if the person isn’t halachically jewish anyways?