People who accept anthropogenic climate change seem resistant to a descriptive label, such as climate change believer. Such resistance is probably part of wanting to be taken seriously, with one's interlocutors focused on the merits of the case and not the qualities of the person making the case.

Of course, it's more than that. The specific label does matter. For instance, "believer" connotes sucker for some - a certain unquestioning quality, a leap of faith. In scientific disputes, you want your position to be based on empirical reality, something that is regardless of how you want it to be. 

The label of "skeptic" isn't so bad, though, because it suggests you're not gullible, i.e.,  prone to belief without rigorous examination of the evidence. Hence, those who "accept the consensus" have been slow to accept the label "skeptic" for those who do not.

I am not a climate change skeptic. Now, what does that mean?

First the framing for an answer, borrowed from Think like a Scientist, Act like a Doctor:

The spirit of science is that of humility. You don’t know for sure. You could be wrong. What seems to be the case may not be the case at all. And yet the scientific project is predicated on hope: you can get closer to the truth through careful application of the Method: come up with testable hypotheses, make sure they’re falsifiable, and systematically test each one. Be transparent about your data and procedures, so others can critique your approach or try to replicate your findings.

Like scientists, medical doctors appreciate their own limitations. Yet they are tasked with making important decisions – possibly life-and-death decisions – despite not knowing for sure they’ve got it right.  Wait and see? Try something? Try something else?  All the while observing and thinking and investigating further. Doctors need to be willing to act boldly, willing to do nothing, and willing to change their minds. Because the health of the patient is what’s important – not a foolish consistency with past opinions.

So it should be when the planet is the patient.