This conundrum can not be fixed. It is fundamental to all government K-12 schooling. There is a solution:
1) Begin the process of privatization with charters, vouchers, and tax credits ( Tax credits are the best option)
2) Gradually move toward expecting parents to pick up the cost of education their own children. In my state the average private school tuition is about $4,000. That is **average**. That means there are schools charging less than that. This is less than daycare. Working parents manage to pay for daycare for their preschoolers but ( Gee!) can't seem to afford private tuition once their kids hit 5 years old.
3) Government would pay out vouchers for schooling only to the poor.
4) In an ideal world, charity would pay for the poorest.
For placement into which school? I am Lutheran. What are the chances that I would want my children to be educated in a Catholic school. Zero.
I just don't believe that a fully fractured system of schools can provide for the needs of all people. Some will just be left out. If there were two Jewish families in a town of 40,000 people, would they have to send their kids to a Christian school that taught religious subjects along with the curriculum, or would they have to fend for themselves?
I bet my seventh grade nun, Sister Mary Victoria, would have found a way for metal working to have reflected Catholic Christian teaching.
Exactly my problem your view of education. There is too much to learn in a short time frame for it to diluted with off-topic material. I know that religious zealots of every color cannot stay on topic for even an hour. A metal lathe can rip people's arms out of the sockets. Keeping the work on topic is actually pretty critical. Naturally, I wouldn't want my kids to learn in a Catholic school. Or a Baptist school, etc. I want the school to be totally religious neutral. That is a worthy goal for conservatives to embrace.
Finally, why do you think you are justified to deprive me an others of my ilk of our equal Constitutional rights? I know for sure that public schools CAN AND DO perform well. They do so in good neighborhoods in well-funded communities. Most of the trouble in public schools is centered around problems created by under-achiever kids. THAT is the fault of the parents, not the schools.