Sometimes, people with similar moral opinions come together and agree to enforce entitlements consistent with that opinion. These are called "rights." While morals can be demonstrated in the state of nature, "rights" cannot be. There are no "rights" without agreements between people, either explicit or tacit.
https://en.wikipedia.org/wiki/Natural_and_legal_rights
Since I'm pretty sure you've encountered the terms natural rights and human rights before, and that you understand that they specify morals without being legal rights, and that we don't basically disagree about how things work, nor do we even disagree philosophically on a wide variety of issues (perhaps importantly that moral absolutism is terrible), I was more curious about whether you think world federalism is a good idea...
To rephrase this, the sort of absolute existence which you seem to be implying for morals and natural rights is only obtainable within the framework of an axiomatic system. And, the process of codifying one's morals within an actionable axiomatic system transforms them into legal rights.
So, I agree that morals express should and should not sentiments. I also agree that individuals can hold morals, in the sense of personal codes of behavior. However, my original point of contention was whether or not natural and human rights exist in the state of nature. A discussion of morals ensued because you implied that an acceptance of the existence of morals was somehow related to an acceptance of the existence of n/h rights.
Morals and n/h rights are fundamentally different in that morals are intra-personal, while rights are necessarily inter-personal. So, while I would accept that morals can exist, in the sense that individuals can desire particular states and derive codes of behavior for making these states more likely to occur, these sorts of morals are not the sort needed to make the functional similarity between morals and n/h rights that you previously suggested meaningful.
These form the key points of our disagreement: that morals act like n/h rights and that n/h rights exist. While you may not have intended to support absolutism, based on the way in which people typically discuss n/h rights, and based on the formal definitions of these terms that I've seen, I'd say that any support of n/h rights is implicitly support of absolutism.
I do understand that it's the absolutists who harp on about n/h rights, I'll try to be more careful about that in the future. It is somewhat absolutist of me to believe that everybody on the planet deserves food, clothing, and shelter in that it's a belief that applies universally, but I won't go so far as to say that you should adopt my beliefs simply because it's somehow incorrect for you to have other beliefs, nor do I expect that our laws will ever satisfy this ideal.
Though, through morally-guided action you can possibly cause the n/h rights which you believe in (but which don't exist) to be reified as legal rights. Now, given sufficient capacity for force, I may still subvert those rights, but through their codification they have nonetheless gained existence.
The second part of your second paragraph actually closely matches my stance. And, it's precisely the prevalence of (implicit) absolutists who continually frame arguments founded on the assumption that some n/h right or another exists that leads to my irritation when these terms are used (relatively) carelessly. Such arguments are fundamentally flawed and, yet, continue to dominate most discussions concerning politics and economics.
Or, might makes legally right, belief makes morally right.
It's interesting, because if you look back far enough you'll see I had the opposite argument with somebody else, where I was explaining that force was the only thing that caused legal rights to exist, and he was accusing me of immorality on that basis.