Actually - if they were assimilated, then they would be seen first and foremost as Polish, not Jewish. The two aren't incompatible, but the primary identity would be Polish.
Are you suggesting that there is a direct link between language used and religion in Poland? That by speaking Polish one erases their given religion.
It's a whole other thread, but there's certainly something about Catholicism that lends itself to rampant nationalist fever. The Utashe knew a thing or two about that...