Notably, the law professors' first argument is that Hobby Lobby in no way compels this kind of exemption:
[T]he Supreme Court's opinion in Hobby Lobby and order in Wheaton College do not compel in any way the inclusion of religious exemptions language in an executive order prohibiting discrimination against LGBT employees of federal contractors. Both actions were predicated on the Court’s belief that the government could fully realize its compelling goals of furthering women’s health and equality through other means – because it could arrange for alternative contraception coverage for affected employees, who then would suffer no harm as a result of an employer exemption. By contrast, there is no such alternative here. Exempting religious employers would harm LGBT employees and it would frustrate the Administration’s compelling interests in providing equal rights and protection against employment discrimination for LGBT people, particularly in taxpayer funded situations.This is essentially the same point made by Professor Althouse, which sparked our discussion.
For the contrary view, see this earlier letter from the Institutional Religious Freedom Alliance. As the law professors' letter notes, however, the IRFA letter cites no authority for its core assertion that religious employers are "free under Title VII to maintain a conduct standard that reflects their religions’ sincerely held beliefs, which include deep convictions about human sexuality." Instead, Title VII merely allows "religious organizations" to prefer people of their own faith in hiring.