On the contrary! B-schools are increasingly giving importance to the non-profit sector, as well as to CSR. You will bring a very valuable perspective which will be very different from what a Goldman guy will bring in. And if you llok at the class stats of the top b-schools you will notice they take in people with Humanities background (if this is what you have).
What will really matter is: whether you took up some real responsibilities and made a positive impact on the people you were working with. You will also need to articulate clear career goals and the need for an MBA to fulfill these goals.