They fought the system because of their religious beliefs and now they are fleeing from the consequences of that flight. I think that fact helps their case in a political asylum argument. We offer political asylum for people who face persecution in their home country for practicing things we consider basic rights here in the US. Being able to raise your children in your belief system with only minimal government interference is something we consider a basic right.

Americans by and large I believe would support them standing up and refusing to give in. If they refuse to give into their government and send their kids to public schools are they at risk of having their kids taken away from them? If the answer is yes, and it from the article is seems to be so, then I would say the threat of having your kids taken from is grounds for asylum.

Keep in mind the US began as a bunch of Europeans fleeing because they were not allowed to practice their religion in the manner they wanted to. That is still important to us.