There are many ways that outrage can be fake, and a variety of them apply to this situation. For one thing the conservative talking points were all about a sense that the feds were coming for your freedom, and not in any way about the merits or otherwise of being able to burn gas in the place you live. For another, this was being talked about as something that would impose a heavy burden on normal people, which is simply not supported by the facts, both because none of the plans that have been put forward involve forcing you to buy a new stove, and because most normal people already have electric stoves.
By the way, I don't know if you actually read or listened to that segment, but it makes clear that there is a real possibility that this could be regulated. Calling it "fake outrage" is not to say "they're making up the possibility that it could be regulated", but "they're blowing this (real) possibility out of proportion, ignoring the reasons it might be a good idea, and instead making up vague and manipulative reasons to object to it".