I think it's fair to say that the Mormon church (not only the membership, but church leadership as well), has a large influence in the state's government and its laws and rules. The church also takes positions on certain social issues from time to time in what I assume is a play to influuence policy both in and out of Utah. For example it recently it came out against family separations at the border. However, to my knowledge the church has never taken a stance on public land transfer, whether it be by scriptural interpretation or through a press release.
True, the Mormon Utah delegation is pro transfer, but I don't see any evidence that it is at the direction of the Mormon church. If it was how do you explain Senator Udall (NM) or representative Simpson (ID) or Senator Reid (NV)? I guess they're dissident apostates destined for a lesser degree of glory (Mormons will find that funny).
To say that “Mormonism like Islam, at the fundamentalist level is a self-serving political agenda hiding behind the protections of relevant religion” is disingenuous at best.
We have to be able to separate the beliefs and actions of individuals who belong to an organization from the organization itself.
For the record I am LDS, you'll find me at church on (most) Sunday's, I disagree with my Church's stance on more than a couple of issues, I’m familiar with the history of my Church both good and bad, and I'm vocal when I think they're on the wrong side of something. However, in all my years attending, and after all the positions I've held, I've yet to come across a nefarious plot to disinherit the people of the United States of their public lands. But then again I’ve never been one of the cool kids, so they’re probably keeping me out of the loop on purpose.