Intellectually, one can only sustain the orthodox position against marriage equality if one assumes that gays are not fully human or somehow defective. Unfortunately, biology contradicts that notion.
The Church is correct in asserting the freedom for the organization and its members. However, our liberty ends where it begins to take away the liberty of others.
Democracy is no license to discriminate minorities. The founding fathers referred to that as the tyranny of the majority.
If the brethren only spend two hours in the Harold B. Lee Library, they would learn that same gender attraction is a natural phenomenon, which includes species ranging from insects, reptiles, birds, and mammals, including all the primates.
The brethren would also learn that homosexuality is not any more problematic than heterosexuality. Sexuality is a challenge, to be sure, but sexual orientation does not exacerbate these problems in any observable way.
The brethren have tradition on their side but facts are a stubborn thing. In a free environment, this conflict cannot end any better than a struggle in favor of flat earth geography.
If one believes in God the creator then the creation is His most awesome revelation. Ignoring the scientific consensus in favor of debunked tradition puts short term political success ahead of long term self-interest, to say nothing of the suffering that we are causing our children and neighbors.
As disciples of Christ, we have an obligation to tend to the wounded in the gutters of society. The Savior formulated that obligation to illustrate the meaning of neighborly love, which is the very essence of Christianity.
There is no other commitment that can suspend neighborliness without compromising our discipleship.