There’s no correlation between believing in individual rights and believing in the rights of Nazis to kill other human beings.

And I don’t see your dichotomy between individual rights and moral rights. They are not exclusive to one another whatsoever.

And to your last point, there’s a lot of good reasons to be moral: (1) genetics, (2) altruism, (3) social incentives, (4), reciprocal incentives, (5) feel-good incentives, (6) long-life incentives, etc.

Look into them. Volumes have been written about each point.