My suggestion would to be always refer to groups of people by a name or designation they choose for themselves.
A separate case in point: People who are for further restrictions on abortion refer to themselves as pro-life. People against further restrictions on abortion consider themselves pro-choice. Both groups present themselves as being for something, but in reality you could just as easily define them as against something, instead. Both groups attempt to define the other in the negative manner routinely.
But in order to give all groups a fair amount of deference in either questions or answers, how groups of people ought to referred to should be drawn from what the groups themselves say they are.
The example from the OP I believe is on point. People who are for stricter voter ID laws in general would disagree with being referred to as "voter suppression advocates" and do not present themselves as such.
"What about all of the outlandish cases of <insert group here> who say they are for <good thing> but obviously in reality truly stand for <bad thing>?"
I don't think it matters. If a group of baby eaters presents themselves as "Population Control Enthusiasts," refer to them as "Population Control Enthusiasts." I would expect a good complete answer including information about them to point out that a by product of enthusiasm for their chosen form of population control is sometimes babies get eaten. A good question may ask why people refer to themselves as Population Control Enthusiasts when in reality all they seem to do is eat babies.