Regulating Homeschooling?

Talk to Action gives an excerpt from this forthcoming paper on homeschooling. Key paragraphs:

Surprisingly, the social and legal implications of this phenomenon have received almost no scholarly attention. For decades political theorists have worried and argued about what steps a liberal society must take to protect children being raised in illiberal communities. They have focused their attention
on the extent to which a liberal society must permit or condemn such practices as polygamy, clitoridectomy, and child marriage.
Virtually absent from the debate has been any discussion of the extent to which a liberal society should condone or constrain homeschooling, particularly as practiced by religious fundamentalist families explicitly seeking to shield their children from liberal values of sex equality, gender role fluidity and critical rationality.

. . . .

Legal academics have been even more silent in the face of homeschooling's dramatic rise. Most articles about homeschooling have focused on the narrow question of whether public schools must permit homeschooled
students to participate in extracurricular activities. Very few have provided any critical evaluation or assessment of current homeschooling laws more generally. None have addressed the significant constitutional questions raised by state abdication of control over homeschooling. This paper seeks to begin to fill this important void. The paper explores the constitutional limits the state action doctrine puts on states' ability to delegate unfettered control over education to homeschooling parents. It argues that states must--not may or should--regulate homeschooling to ensure that parents provide their children with a basic minimum education and check rampant forms of sexism.

I don't know a lot about the homeschooling movement, although it is interesting, as the paper points out, that this movement started as a left-wing phenomenon as a part of the free schools efforts in the 1960s. I'm not sure how one could argue for regulating homeschooling without regulating private schools (and choice schools) which seem mostly unregulated (from a pedagogical standpoint at least) in Wisconsin as far as I can tell.