How much evidence do conservatives need to contradict the scientific consensus on an area of science?

Not really any. Evidence can always be ginned up - it may be irrelevant, or false, or silly, or even legitimate. That doesn't particularly matter. The modern right wing movement is pretty much a cult, and it works the way any cult does - it tells people what to believe, and the followers believe what they are told. If there is contrary evidence, the follower can always create a good rationalization for the doctrine in question - this works extremely well, since the smartest followers, the ones who are likely to really understand how bad the evidence is, are also the ones who will be most inventive in finding rationalizations for believing anyway.