<em > A. Don’t keep the community’s level of chumrah (ex. maybe a mainstream Lakewood school refusing a child whose mother wears bright colors.)
B. Don’t keep some actual halacha. (ex. shabbos. Or doesn’t cover her hair).
I can tell you of some more modern yeshivas who WILL take kids from homes who are NOT Shomer Shabbot and NOT even Kosher and even these kids will become religious.
It is just as likely that a kid from a non-religions home (especially younger ones) will be influenced by religious kids and rabbis than the other way around. I know PLENTY of people who fall into this category