It's pretty hard to pin down what natural rights are. That a society ought to consider the limits of normal human behaviour I don't dispute, but that just informs the rights a society grants its members. Rights are still a human social construct.
We value our safety from, e.g., rapists more than the rapist's liberty.
If human nature is ultimately "not controllable by law", then that would certainly apply broadly, not just to cherry picked aspects of it.
Certainly assault, murder, rape, theft, harassment, abuse, cheating, and the like are facets of feral humanity; just as much as positive traits like self-preservation, compassion, parental instincts, social bonding, etc. Law usually stands in a directly contrary position to the former list, to wide agreement.
From our own human nature, actually. Think about this for a minute. Would a normal person be willing to believe something because you were forced to? If someone was violently attacked, would they not fight back?
By recognizing these aspects of human nature as something fundamentally not controllable by laws, we can instead force government to work with that human nature instead of contrary to it.
Now, the current conflict is being caused by pitting these against each other. Because people believe they are unsafe because of people who own guns or use hate speech, you now have two groups of people who believe that the other group is making them unsafe.
This is ironic, because we're actually becoming statistically safer over time, but it does lead to some very real conflict because people believe there's another group out there that wants to harm them, instead of realizing that both sides really just want to protect themselves, barring a few fringe whackos on either side.