It does. That is one of the very limit content regulatory powers it has over cable tv. “Obsenity” is a very high bar, though, and is, itself, not protected speech under the 1st Amendment at all.

To be considered obscene, it must meet a three-pronged test from the Supreme Court:

1. It appeals to the prurient interest.
2. It depicts or describes sexual or excretory conduct in a “patently offensive” way.
3. Taken as a whole, it lacks serious literary, artistic, political, or scientific value.

Basically Brian Kilmeade can’t show his gaping asshole taking a dump on Fix & Friends. But he can casually suggest euthanizing the homeless population and it’s out of the FCC’s hand.