I think the best recourse is to flip the script about what is non-negotiable. I think the best answer is to instead weaponize that ethos against them.

Human rights are good because I said so. Your (their, as in conservatives) view on human rights is wrong because I said so. Why is it right when I say it? Because I’m not conservative and that makes my beliefs more important and more correct than yours (theirs). And because you (they) don’t agree that human rights are non-negotiable, you (they) are objectively bad and thus your (their) argument is now moot.

Now this doesn’t exactly solve the problem and it is of course subject to the same systemic failures that conservativism has so lovingly adopted. But it should at least be able to fight back.