Liberals want to follow the standard definition of federal supremacy, i.e., states can pass laws that don't contradict ones that exist at the federal level. FCC abandons the federal law = states can pass their own law.
Conservatives, on the other hand, want to cherry-pick when following federal supremacy is okay and when ignoring federal supremacy is okay. It's okay when it's an issue that aligns with conservative interests and it's not okay when it doesn't. So in the case of the FCC, they're trying to have it both ways at the same time: abandon the law and then try to prevent states from filling the void. It's an attempt at reverse federal supremacy, i.e., "no federal law exists but you can't make a state law either".