Proponents of a minimum wage need to believe that in this particular case, raising a price does not proportionally decrease demand. While this may be true (economics ain't physics), the burden of proof lies with the proponents, since it would be a contradiction of probably the most well established "law" of economics.
If you feel that the data in this and similar studies are inconclusive, to the extent that you respect the discipline of economics, you should oppose a minimum wage.