Elder Oaks, in 1992, stood before part of Congress as a representative of the LDS church and said, "we would prefer that the Supreme Court reverse the Smith case and restore the full constitutional dimensions of the First Amendment protection of freedom of religion." The link is here (scroll halfway down for the specific article).
I'm oversimplifying, but the Smith case was basically about whether members of a religious group could engage in religious ceremonies that involved peyote (an illegal drug). The majority ruled against the religious group, and thus against the freedom of religion.
What's most interesting here (besides the fact that the LDS church wants these people to be able to use peyote for religious purposes) is that those who voted for religious freedom were liberals, while those who voted to restrict religious freedoms were conservatives.
In other words, the LDS church, when dealing with religious freedoms, is decidedly politically liberal.
Scalia, Rehnquist, White, Stevens, Kennedy, and O'Connor all voted to restrict religious freedoms. Scalia, Kennedy, and O'Connor are all conservatives, placed on the Supreme Court by Reagan. Stevens was appointed by Ford (a Republican) and is usually seen as liberal (although sometimes, like here, he doesn't vote that way). I don't know much about White, but from what I can tell he was neither conservative nor liberal.
The dissenters--those who agreed with Elder Oaks and the LDS church--were all liberal. They include Blackmun, Brennan, and Marshall. Marshall was a liberal, put in by Johnson. Blackmun, put in place by Nixon, started conservative but became quite liberal (and was firmly liberal when the Smith case came along). Brennan was the leader of the liberal wing of the Supreme Court, placed there by Eisenhower.
It's obvious that both political parties have good parts, and both have bad parts. The church keeps repeating this, but I'm not sure it's getting through to the majority of the members. It's clear, however, that the liberals on the Supreme Court are more interested in protecting our religious freedoms than the conservatives.