1) Public school for free for middle-of-the-road (in our district) results, and be at the mercy of school-board politics,
2) Do Catholic school, and we agree with the religious particulars of the Catholic school near us, but it's expensive and they may be weak in STEM and global social studies,
3) Join a home-school co-op, and use the flexibility and extra time to get it all right and fill in any gaps.
I don't know what the right answer is, but 3 is looking increasingly good.
I went to a Catholic school in Ireland and religion had a very minor role in day to day activities or the curriculum.
Any religious activities that did occur were entirely optional; nobody cared if you participated or not.
They're really called Catholic schools because they used to be run by people from religious orders, but they're all dead now and have been replaced by lay people.
Unfortunately, looking from the outside in, the teachers care but the administrators do not. While I would still consider public school, I think supplementing and supervising their assignments is the minimum a parent can do. Homeschool just isn't feasible for many people, and there is a reason teachers specialize in topics past grade 5.