I've seen some non-plausible "what-if" theories about how letting Catholic-owned businesses deny contraceptive coverage to their employees would lead to other religious business owners carving out other unacceptable exemptions in health care.
But here's a plausible possibility. Jehovah's Witnesses teach that blood transfusions are unacceptable.
From Wikipedia...
Jehovah's Witnesses believe that the Bible prohibits ingesting blood and that Christians should therefore not accept blood transfusions or donate or store their own blood for transfusion.[1] Watch Tower Society publications teach that the Witnesses' refusal of transfusions of whole blood or its four primary components—red cells, white cells, platelets and plasma—is a non-negotiable religious stand and that those who respect life as a gift from God do not try to sustain life by taking in blood,[2][3] even in an emergency.[4]
That is as real a dogma to the Witnesses as contraception is to Catholics.
What if a Witness business owner wanted to insist his or her employees health insurance not cover blood transfusions? That would be a serious gap in coverage, and yet the matter is a serious religious principle to the Jehovah's Witness and paying for transfusions might well violate their principles.