There is an argument to be made that Twitter is a public forum and subject to free speech protections. This isn't an argument I agree with and is the domain of hardcore leftists, but there is that argument to be made.
In defense of ldsfaqs, I think we can acknowledge the right of a private business to adopt certain policies while simultaneously criticizing a business for the policies it adopts. This is no different than believing that the LDS Church ought to be able to refuse to marry homosexual couples while also believing that the Church is contemptible for doing so.
It is not uncommon to argue that private forums should have be animated by free speech principles while also thinking the private forum ultimately gets to decide what it wants to do for itself.