Many native Portuguese speakers are unaware of this, and they will sometimes insist that the choice of word depends on the person you are speaking to, and that it would be considered rude for a man to say ’obrigado’ to a woman.  However, I would strongly recommend that you stick to the ’correct’ way of speaking - men only say ’obrigado’, women only say ’obrigada’ - unless you happen to live in a region where the locals will be offended by this!