It’s rather sad that we have to assume that every Catholic institution, including the Nashville Dominicans, employs people who use contraceptives.
Catholic Charities, for example, probably wouldn't even qualify as a "religious organization" by any objective measure. One reason for this is that it doesn't require its employees -- or even its leaders -- to be Catholic.
Most Catholics use contraceptives and have since the 1960's. That's why Catholics no longer have big families. The use of contraceptives is no longer an issue for most Catholic women.