Meanwhile, even the original Central Hudson test --- if commercial speech concerns lawful activity and isn't misleading, the government (1) needs a substantial interest and (2) must narrowly tailor the restriction --- was inhospitable to the sentiment in this blog post. But Central Hudson has as I understand it gotten more restrictive, not less; for instance, Sorrell, which was a bipartisan decision, applies heightened scrutiny to regulations under Central Hudson.

You can keep cigarette ads out of Highlights for Kids. But you're not going to be able to keep Nike from buying up ad inventory, and you'll certainly not be able to regulate political and cause advertising (and "propaganda").