I've only ever encountered "Do you have a problem with that/x?" as a challenge. Can it be used otherwise? Probably, but a native speaker would know how it's going to be received especially in a contentious topic like politics.
If I thought the other person just wanted a fight, I'd ignore them. If I thought a good discussion might be had I'd go something like
"I think X and Y is good evidence of A. Why do you think that isn't the case?"