A view that I've had for a while now is that there are no moral obligations, only legal ones and other social obligations (by 'social obligation' I mean like you are obligated to follow your job duties or you will be fired). Obligations are social constructs. I don't believe in moral rights—there is no intrinsic 'right to life.' Rights are something a state grants a citizen. Rights can be taken away. If someone has a seizure, their right to drive is taken away until they have been seizure-free for 6 months. Your right to life is taken away when you try to kill someone. Etc. However, we can have discussions around what rights a state should grant its citizens. You could argue that it would be objectively better for a state to grant a right to produce alcohol compared to a state that bans alcohol, because banning alcohol leads to all sorts of problems (as America discovered in the Prohibition Era). In this sense there are objective rights.
The reason why I don't like moral rights is because I can't make sense of them. I don't believe anything can be magically right or wrong. If an action is right or wrong, there will always be an explanation for why this is the case. You could say I believe in a moral version of the principle of sufficient reason. In fact, I suspect that morality necessitates this—it is necessarily the case (i.e., the inverse is impossible) that for any moral fact, there is an explanation for that fact.
But if someone has a moral right, then violating that right is wrong. But how is it wrong? What's the explanation? Moral rights sound like these magical things that people have, but there is no explanation as to what they are or where they come from.
This is one reason (of many) why I like consequentialism. I don't have to worry about trying to make sense of moral obligations or about explaining why violating someone's right is a bad thing. (Certainly, violating someone's legal right is often a bad thing for consequential reasons.)
Importantly, I think we still have objective morality without moral obligations. Moral facts don’t need ‘em. You have something like obligation when it comes to epistemic normativity. You ought to reason well, you ought to think rightly, you ought to believe what's true, and so on. If we call those epistemic obligations, I think that's fine. We are still demanded by normativity to not make mistakes in our reasoning, and we can apply reasoning to moral contexts to produce moral reasoning. Just as reasoning can be objectively good or bad, reasoning applied to moral contexts (moral reasoning) can be objectively good or bad.
(There's a good question you can ask about the nature of normativity's demand, which is basically the question of why should we care about being rational, or why should we oppose irrationality. But I'll save that for another time.)
If we call epistemic obligations applied to moral contexts moral obligations, then I'm fine with that idea of moral obligation, but you aren't violating anyone's intrinsic rights in the case that you violate these moral obligations—you would just be violating your epistemic, normative obligation to think rightly, reason rightly, etc.
Anyway, I'm excited to have discovered a philosopher who is a hard consequentialist like me and feels the same way I do, at least roughly, about moral obligations: