Such a declaration would give official government protection to any individual, company, or organization openly discriminating "on religious grounds" against LGBT Americans as well as others engaged in non-traditional lifestyles like heterosexual unmarried cohabitation.
Quoted in The Washington Post (link here), Lambda Legal's chief executive said such an action would be "an invitation to theocracy. It is the privileging of some religions over others, and an invitation by members of those religions to flout the law."
You should read the complete text of the leaked White House document, which is available online at The Nation (link here).
But, hey, Donald Trump held a rainbow flag upside-down for two seconds, so we shouldn't worry about all this constant rhythm of dropping shoes, right? Wait a minute -- what's that handwriting on the wall over there?