Reb Moshe Feinstein allowed teaching patrilineal kids in a community day school setting.
R’ Aharon Soloveitchik allowed a pluralistic day school in Chicago, and his brother admitted such children into Maimo, according to Rabbi Asher Lopatin (he says he has this on tape).
This would definitely be an issue to look at, and you may want to cite Zera Yisrael as a case study.
Another issue would be allowing the secular to drive on Shabbos- look at the machlokes between Reb Moshe and Rav Soloveitchik; the Rav was machmir on this.