Rights are legal creations and if the law changes, your rights change. Over the last few centuries, you've lost your right to own slaves and you've lost your right to torture animals but you've gained a right to abortion and if American you've gained a right to have a Miranda caution read you after being arrested and a right to have a free lawyer if arrested.
Who knows what rights people will and won't have in 300 years...all these things are very fluid.
Problem is, what you are calling "rights" are just laws. Slaves always had rights. They were just denied by law. Women always had rights to engage in any activity that men did. They were just denied by law. Gays always had the right to form and consumate relationships. They were just denied by law. As the Declaration says, all men are created equal with certain inalianable rights. Those laws I mentioned changed not because society decided to change rights on a whim, but because society realized those people had rights all along, and denying them was unjust.
That's the part you seem to have a hard time grasping. Rights come from people reasoning and figuring out what is just. Laws are applied to the best of peoples ability to protect those rights. But often, people have skewed sense of entitlement, and create unjust laws. Those laws don't change the underlying rights.
300 years from now we will very likely have debates about entities some don't consider human. There will be attempts to pass laws denying people rights, such as attempts to ban marriages between a human and, say, a clone, or a human-animal hybrid (furry), or an intelligent machine/robot. Conservatives, and especially religious ones, will proclaim loudly that those "things" are not people, they have no souls, and giving them rights will take us down slippery slopes (What's next? Incest? Marrying a full animal? Marrying a toaster? Giving your refrigerator rights?). But even if the laws are passed, and those personal choices are interfered with, the fact that those "things," if they are able to think, reason, and feel, still have fundamental rights, will still have their rights of making their own reasoned, informed, and personal choices infringed upon by law.
I'm not sure how to explain this better besides asking you to think if slaves were entitled to rights while slavery was illegal.