Not bloody likely. Now you've just put them in the same group as the other conspiracy theorists, and given them the additional (legitimate) ammo that "the establishment is censoring them".
Confirmation bias is a hell of a drug.
Additionally, (and this is just a personal feeling), but something about top-down "reducing airtime from fringe views" feels very wrong. Who decides what a "fringe view" is? By that rubric, Creationism is perfectly legitimate since it's widely held.
I think we'd all be better served, morally as well as practically, by letting the loons be loons and let people make their own decisions rather then trying to explicitly control who gets airtime. Bring on the denier and let them get annihilated in a debate against someone who knows what they're talking about. This has the benefit of not invoking censorship boogeymen (which may or may not actually exist) and doesn't hand over the "we're being oppressed" card to them.
Is it true for the US? That's definitely not my impression for Europe, it always looked to me that was a belief from a tiny minority.
Amongst 1) the general public, 2) scientists in general, or 3) climate scientists specifically?
EDIT: Added the word "fringe". As in, a conspiracy theory that doesn't get media coverage.
"Satanic Ritual Abuse" aka Satanic Panic also had a field-day in the courts, if not the legislature.
The tide seems to be turning, but until quite recently, it was an article of faith (literally, on occasion) among many conservatives that climate change was a liberal-media bogeyman. This was true even among the more respectable conservative publications and commentators, and not just the wackos.
In terms of science we can.
In terms of politics or society we can not, but we can distinguish political reporting from science reporting, even on a scientific issue which has political implications.
By no means am I suggesting it's a legitimate movement or a non-fringe movement amongst scientists, or that it deserves equal airtime. The viewpoint is largely bunk. Its adherents, however, are legion.
There certainly are other senses of the word "fringe", some of which they fit, others of which they don't.