Let me give 2 hypothetical examples related to homeschooling.
If a family were homeschooling their children, but ONLY taught them to read, so that they could read the religious text of their faith, and didn't also teach them to write, do math, science, geography, history, etc-- THEN a family could be found to be educationally neglecting their children thru the homeschooling process.
Or hypothetically, let's imagine a family claiming that they are homeschooling, but they don't actually teach their children anything at all, and the children, who are mentally capable of learning, can't read or write, do math, etc by a reasonably comparable age to other children. THEN a family could be found to be educationally neglecting their children through homeschooling. Even if that family claimed that they were using "oral traditions" to teach their children.
The laws on homeschooling vary from state to state, but in common, they require parents who homeschool to teach their children to read, write, do math, etc. In my state, for example, if you do not have a bachelor's degree, you are required to meet more stringent requirements than a parent with a bachelor's degree or higher. IIRC, parents without a 4 year degree have to use a certified curriculum of their choice, and register that, as well as submit results of standardized testing periodically. If you do have a bachelor's degree, or higher, the laws more loosely define the requirements. (I haven't checked the actual wording in a while, so I may be a little off on this.) One of our kids is partially homeschooled for certain core subjects, so we had to do some research years ago to persuade the school district to get on board with our plan. We still have the district give this child the regular standardized tests in those subjects that everyone else takes, as a mechanism to officially document her progress in the homeschool curriculum we use. (They were quite happy with that part of our plan, lol!)
We haven't heard anything from officials that this Stanley case has anything to do with homeschooling. And indeed, it seems that 2 older kids have achieved college admission, so we can be at least reasonably sure that there is effective homeschooling going on in the home, unless something has changed drastically in recent months/ years. So, IMO, its a deceptive claim and a distraction for him to say that they are being persecuted simply because they are Christian homeschoolers.