If the First Amendment allows children to traffic in snuff films, Nazi regalia, bomb making manuals, Satanist tracts, classified nuclear information, and so forth while in a government school, it's safe to assume that COPPA is an unconstitutional prior restraint on free speech. I am astonished that the ACLU has not already handed the FTC their ass.
"The ACLU has long been strongly supportive of COPPA. It is an important first step on the road to universal baseline privacy protections that ensure that every American—young and old—has meaningful control over their personal information online. (...) The ACLU protects privacy and free speech simultaneously, and the two interests are rarely at cross-purposes. Right now, COPPA is a great law and it does both effectively."