There is evidence of "morals" because people espouse them; I'm not sure how you could contend otherwise. That's not proof that they're right or wrong, merely that they exist.
Natural rights theory is simply a moral affirmation of an innate desire to live in accordance with one's will. Natural rights are NOT invisible force fields that are supposed to protect you from all transgressions. It's a moral concept that is justified by a set of biological and psychological axioms.
Otherwise, it's just a bunch of mindless, fanatical handwaving nonsense.
I can just as easily come up with a handful of other examples, without even trying very hard.
I have the right to own a gun; I choose not to exercise this right.
Many people have the right to vote and choose not to- I think that in an average election year, less than 60% of eligible voters actually vote. This last election, it was a little more. 66%, maybe?
People in the US have the right not to be physically assaulted, but some of them choose to enter into consensual S&M relationships and voluntarily forfeit this right.
The list goes on.
If we exercised every right we have to the fullest extent, we'd have no time to do anything else but go around exercising rights all day long, to no purpose.
Rights are there to be exercised if and when you need them.
"Morals" are a social construct.Like there's concrete evidence of behaviors and other naturally occuring 'phenomena'.
They are something we evolved to allow us to live together in groups; to allow for there to be tribes, communities, civilizations.
They are all based on the law of reciprocity ("Do unto others", Golden Rule, etc), and have their origin in prehistoric times, and are more or less universal: common to every nation and culture. Without reciprocity-based "morals" or rules, cultures don't last long enough to be more than a blip on the radar of history.