No, because “property rights” is a broad term. It doesn't mean that you have to be an anarcho-capitalist to believe in property rights (though anarcho-capitalists would disagree, of course).
There can be a constitutional right that the state is only allowed to interfere with your property by levying taxes on your income and has to accept payment in the legal tender – which would prohibit the state from confiscating your “precious” (in the words of Gollum). This would be considered “property rights” (though in practice, property rights are narrower; e.g. “eminent domain” etc.).
Now, should anarcho-capitalists move out into the woods? That doesn't really help, they are still subject to the state's laws, which conflict with the anarcho-capitalist conception of property rights (any restriction of hunting on unowned land is illegitimate for the anarcho-capitalist), and, theoretically, taxes. They probably have to move to a true no-mans-land, like Antarctica.
But if they live in a society, they must accept they have entered a contract, and that contract implies that there is a debt to be paid.
I don't really think that anyone has entered a contract just by living in society. Using the state's services can't be realistically considered consent – because it can't be totally avoided: the anarcho-capitalist may not want to use the state-built road in front of his house, but it's just there! So from a moral standpoint, it truly is forced upon people to pay taxes. No need to sugarcoat this.
But even the most libertarian (stable) societies retain an element of coercion to cooperation by force. The overwhelming majority of people want to live at least in a minarchist state, whose services have to be paid for. And it is simply a consequence of the free-rider problem that there cannot be a way of opting out of that. Most people accept that, so most people are not anarcho-capitalists.