RebE, having acceptance standards is somewhat different from expelling. Same difference as between rejecting a shidduch and giving a get.
But even them – a number of chabad schools accept such kids at least in younger ages, especially Israelis who send kids to Jewish kindergartens until public schools. And now, with government giveaways of pre-schools that seem to also fund religious ones, I’ve heard of mixed kindergartens of yeshivish and non-observant kids. Possibly because free beats the concerns and nobody issued an issur yet (as with public schools).