Am I obligated to contribute to society?

Yes, in the form of the taxes you'll pay to support the commons.

Only if you want anything from that society.

I think that you are.  Society has given you many wonderful things and you should contribute back again.  This is why I am an unabashed communist.  "From each according to their abilities, to each according to their needs".  Strangely the more you contribute back to society the more society has to offer you and everyone else.  So in a very real way you get more back by contributing that by simply attempting to take something that you have never earned.  "Ask NOT what your country can do for you.  Ask what YOU can do for your country".

If you are living in a society, you must contribute according to your capacity. because society has provided certain things to you for which you should adequately compensate it.

not if you're black