They are all part of the same thing. You have the right to use your voice (or other means of expression) as you wish, too. Both rights are about doing what you want with what is yours.

How exactly WOULD free speech interfere with property rights?


Because those others are not the same kind of rights. There is no natural right to things that might be possessed by another. Natural rights, like freedom of speech & worship & action and property, do not require the surrender of others' rights. Your hypothetical rights to health care & food & the like presume a right to take those from others. The right to property does not. As long as everyone's property or natural rights are respected, they do not infringe upon others' property or natural rights. You cannot say that it is possible to grant everyone food, shelter etc, without violating the natural or property rights of others.

Declared by whom? What source? I do not acknowledge those, because they are not rights, they are offers of gifts. Your disingenuous attempt to legitimize those fads by juxtaposing them with natural rights does not change the essential nature. The rights to property & liberty require others to back off. The rights you mention require others to give. No one has the right to demand action of another, which is what those BS rights to shelter, health care, etc. assert. Property rights merely demand that no one interfere with the owner's rights to do as he wishes. They do not demand that others subsidize his property or contribute to make his owning it possible. In other words, natural rights are more like restraints upon how others may act upon you, whereas your made-up rights are demands of actions by others. There is no legitimate basis for demanding people supply those things, and they would all require the intervention of an outside force. There are no natural restrictions on human freedoms. There is no restraint upon action or speech or use of property that does not occur without human intervention. On the other hand, a man alone in the wilderness has no way of being provided with his so-called rights to food, shelter or health care. He is free to speak, act or use his possessions as he pleases, but without human society, he cannot be awarded what you claim are equivalent rights to what he does possess. Where human society is the only thing that can infringe upon natural rights, it is the only thing that can provide your theoetical rights, and thus they are NOT natural.