Questioning established beliefs and fact should absolutely be encouraged. But that questioning must be grounded in a good-faith, logical, reasonable belief that contrary evidence exists. When mountains of evidence are provided that support existing facts, and you are unable to come up with any persuasive evidence or avenues of research to contradict those facts, you are an idiot and have no place influencing or making public policy.

And what about the cases where there isn't a mountain of evidence supporting one side or the other?

At least from my observation, the general stance of most people is 100% complete belief in any partisan theory, and complete rejection of any opposing ideas, regardless of the amount of evidence supporting each.

Well, duh, then there's more room for doubt.

Look, we're talking about the difference between opinion and fact here. By its very nature, "fact" implies that you have enough evidence already that questioning that fact requires evidence of its own. If I hold some weaker opinion, then sure, it's entirely reasonable to hold an opinion contrary to that without the burden of proof immediately being on you.