[…] Anyone stupid enough to believe obvious rubbish doesn’t care what your source is.

I do understand your point, I think. I’ve had an ongoing quandary regarding how one should effectively debate irrationality. But I still personally believe that one’s allegiance to the truth is a matter of principle rather than a matter of pragmatism. I think sources should be cited not necessarily with the intent of using them as ammunition to prove an argument, but mainly for one to ground themselves in evidence based thinking.