My obligation is to contribute to the society I live in, not to support the government I live under.

There's a huge difference between society and government. Some or many of the ills of our day can be attributed to the fact that too many people confuse the greater good (society) for the lesser evil (government).

So no, no one is under any obligation to pay tax to a government. A government may coerce you into paying but that still doesn't mean you're obligated. But all decent human beings do have a desire to contribute to the community of people in which they live.