Where to begin
Concern for the planet's ability to support life wasn't always a "leftie" issue. Teddy Roosevelt was a Republican, and he founded the National Parks system. The Clean Air Act and Clean Water Act were signed into law by president Nixon, of all people. How the "liberal left" inherited it, I think, is by the infiltration of "the right" by corporate special interests more concerned with the next quarterly report than by long-term consequences. Just an opinion there, no supporting data.
The ability of the planet to supply fresh air, clean water, and other life support would sensibly be a centrist issue, I would think.
Regarding the perception of hysterical treatment of "climate heretics" -- yes, some of that goes on, but maybe some of it is also panic? If person A's foot-dragging is perceived as the doom of person B's descendants, might not person B be excused for a bit of exasperation?
As to a "left wing conspiracy" -- I haven't seen anything specific proposed yet. I have seen evidence put forth of a corporate conspiracy -- not right wing, although it seems to hide under and manipulate the right wing -- to distort the debate on climate change. See the Union of Concerned Scientists' web site, and scan for mentions of Exxon corporation. www.ucsusa.org.
Finally, suppose for a moment (in turn) that each side of the argument is dead wrong, and we react wrongly to the evidence. First, suppose that human-caused climate change is complete nonsense, and we bought it all:
We will have cleaned our air, moved to renewable energy, reduced our dependence on middle-east oil, and generally thought out sustainable schemes for all production. This includes food, manufacturing, recycling instead of landfilling, etc.
Now, suppose that human-caused climate change is real, the tipping point is at hand, and we decided that it was a popular myth to be safely ignored:
Increasing ocean temperatures continue killing off coral reefs, setting off the chain reaction deoxygenation of the oceans. Fairly soon this causes anaerobic bacteria to start farting sulphur into the atmosphere in large quantities; most other marine life dies off. There are the predicted super-hurricanes, drought, etc. For those who live in the eastern US, you can expect to see alligators in the Chesapeake bay -- the clamdiggers will love that. That is, if the marine oxygen kill doesn't cause a large scale extinction event, leaving nothing left but cockroaches and pond scum.
(I'd like to support the oceanic oxygen depletion thing directly, and I believe it comes from the TV program below, but the overview isn't sufficiently complete and I'm not going to purchase the DVD to prove a point.
The point being, it's safer to work against human-caused global climate change and be wrong, than it is to ignore human-caused global climate change and be wrong.