If it's a school that teaches or promulgates religious doctrines, then it should not qualify for the same benefits as a school that doesn't. The refusal to teach or support birth control is in support of a religious doctrine. Therefore a school that does that should be taxed at the same rate as, say, a movie theater or delicatessen. (Granted those are probably different tax rates...taxes are complex and vary wildly by locality. Schools, however, are generally granted a specially favorable tax rate.)
P.S.: I didn't mean to single out Catholic organizations more than other religious organizations, but the article was about a Catholic organization. I would have the same opinion of Baptist, Presbyterian, Mormon or Hindu, Moslem, or Pagan organizations. But it is true that the major religions, especially including Catholics, have taken much more advantage of taxation relief than more minor religions typically have.