Is this about public funding or some other legal mandate required to even operate a school?
It would be one thing just to accept tolerance ... you know like the old debate between religious tolerance vs. religious liberty. But anything that implies a rejection of Catholic teaching cannot be accepted ... even at the cost of having the school closed down.
There might come a time when we have to say "the era of Trad private schools is over" if it ever comes to that.
Just like there might come a time -- if it isn't here already -- where a few faithful priests here and there, a handful of faithful Trad chapels (independent of any group) nationwide is all Trad Catholics can hope for. That is to say, when the era of large organizations like the SSPX being "basically a complete, pretty decent replacement" for the Conciliar Church is over.
In other words, the attitude, "I'm NOT going back to hotel rooms and garages for Mass -- ever! Even if it means giving up my Faith!" can be quite dangerous for a person's Faith. Some people can be quite stubborn in this regard. But they may have to make that very choice one day.
Drawing a red line and saying, "I refuse to ever go any further than THIS from mainstream or normal" can be a recipe for disaster.
The same goes for school. We might have to give up our comfort which allows us to "have our cake and eat it too" by sort-of protecting our kids from public schools while keeping a huge amount of free time and money by not having to homeschool.