They are saying religious institutions should be in sync with their (official) religious teaching, whether Catholic, Evangelical Protestant, Mormon or Orthodox Jewish.

 (Of course, why people would want to work in these religious institutions, schools  --Yeshiva University, Bingham Young, Wheaton College, Notre Dame, etc. -- is another thing, knowing that such institutions abide by a different set of values, standards, ethical evaluations. That is, knowing these institutions' mission statements and policies, why work at those schools if one can't abide by their mission specifications, narratives, declarations, assertions, etc.! The poor Church of England, as an established state church, has to take into account  what Parliament says. But churches in the US are not state churches. The Amish do their thing, for example, without the state imposing cars on them, among other things.)