These regulations were only voted on late in 2016 and never went into effect. To do the regulations, the FCC reclassified the internet as basically ye olde telephone system, which then made it subject to their purview based on laws created in the 1930s. This is classic overreach. Congress never gave this authority to the FCC and is acting to put them back in line with the law.
It's pathetic the the WaPo used their platform to create more heat than light on this, by selective quoting. Here's a more full quote from Rep Blackburn that explains her position more fully.
“The FCC already has the ability to oversee privacy with broadband providers,” Blackburn explained. “That is done primarily through Section 222 of the Communications Act, and additional authority is granted through Sections 201 and 202. Now, what they did was to go outside of their bounds and expand that. They did a swipe at the jurisdiction of the Federal Trade Commission, the FTC. They have traditionally been our nation’s primary privacy regulator, and they have done a very good job of it.”
The lesson here really is that if the issue is really important, then get an actual law passed instead of trying to contort regulatory authority based on laws from the 1930s. The previous president could certainly have done this, but chose not to.