People who claim rights are "just" a mental construct without any external reality often use that idea to lead into a lecture-- with their very next breath-- promoting their ideas of responsibility; often based on their interpretation of morality.
It goes both ways. If rights are meaningless because they are a non-real mental construct, then so are responsibilities.
Humans are-- more than anything-- the mental animal. That something is a mental construct doesn't mean it isn't real. For humans, nothing is more real. In fact, physical things which people can't fit into a mental construct are often ignored; having no "reality" for most people.
So, yeah, rights are nothing when removed from the human mind, but the same is true for responsibilities. Neither a rock nor a corpse has any rights or responsibilities.
I understand why some people are so opposed to rights while being so adamant about responsibilities, but, like it or not, your primary responsibility is to not violate the rights of others.