New proposed regulations "are largely a step backwards for protecting consumers' privacy, particularly in terms of consumers' attempting to stop the sale of their information," the Electronic Frontier Foundation, ACLU and other watchdogs say.

"If the ISPs win this First Amendment argument, it's difficult to see how we're ever going to have any kind of privacy law in the United States," Public Knowledge's Harold Feld says.

"Your very existence is being parsed, split, and sold to the highest bidder, and there is very little you -- or anyone, including the federal government -- can do about it," Sen. Kirsten Gillibrand says.

Clearview AI was hit with another federal privacy lawsuit on Wednesday, and is facing cease-and-desist demands from Google, Facebook and Twitter.