Jim Burroway has the best and most concise argument I’ve yet read on this. Money quote:
Because ENDA contains an explicit LGBT-only religious exemption, the Supreme Court could, in following the Hobby Lobby precedent, look at that exemption in ENDA and conclude that Congress had effectively expanded the RFRA to cover a whole host of LGBT-rights regulations that have come about since the demise of Section 3 of the Defense of Marriage Act, including health care, hospital visitations, spousal benefits, and so forth. The possibilities for unintended consequences are enormous… The concern here is that the Obama administration may lift the language of the religious exemption clause from ENDA and graft it into his executive order, and thereby effectively eviscerate the order’s effectiveness for large numbers of LGBT people.
The Dish 