"Because religious belief, or non-belief, is such an important part of every person's life, freedom of religion affects every individual. State churches that use government power to support themselves and force their views on persons of other faiths undermine all our civil rights. Moreover, state support of the church tends to make the clergy unresponsive to the people and leads to corruption within religion. Erecting the 'wall of separation between church and state,' therefore, is absolutely essential in a free society.
"We have solved ... the great and interesting question whether freedom of religion is compatible with order in government and obedience to the laws. And we have experienced the quiet as well as the comfort which results from leaving every one to profess freely and openly those principles of religion which are the inductions of his own reason and the serious convictions of his own inquiries."
— -- Thomas Jefferson, to the Virginia Baptists (1808).
Something to Consider, Though
There is nothing wrong with choosing to stay-at-home and choosing to homeschool as an option. Where I would get worried over this as a feminist would be in a situation where most mothers would be expected to do that. Because it would mean pretty much that mothers with school-aged children would drop out of the labor force and over time there would be very few women seeking degrees in medicine or law because they'd never get the investment in tuition back, given the shorter working lives and the fact that knowledge gets outdated pretty fast if it is not used. And firms would expect women to drop out for like ten years so wouldn't promote many women. Even fewer than today.
Over time the scenario I paint would mean that there would be very few women in decision-making roles in general. Of course if fathers were equally likely to be the homeschooler this would not happen to the detriment of women. But I suspect the vast majority of homeschool teachers are women. So it is really about the division of labor within the families, as usually.