This strange law does not seem to follow normal conservative/liberal lines. However, it can easily be explained by a state that is controlled by a political machine. In this case, the political machine is a church.
The founders of the LDS Church were politically ambitious. Notably, Joseph Smith declared himself a Lieutenant General. Church President Smith ran for US President and even made the habit of marching around with a militia while wearing a Napoleon outfit.
The politically ambitious leaders of this political machine sought to create a political block. To do this, they sent Missionaries abroad to recruit adherents. They would fund transport to the United States then expect political patronage along with a 10% tythe from the recruits. (This migration is well documented. Here is a study at BYU.)
The ambitious missionary program gave the LDS Church a solid voting block which assured the church's hegemony in local politicals for almost two centuries. Historically, Mormons held 90% plus of the legislative seats in Utah. It fell to over 80% in the 2008 elections.
In Early LDS history, the church focused on creating a political block in the US. In recent years, the Church developed an international strategy:
Since the early 1990s, the Mormon Church has surpassed 13,000,000 members worldwide. Much of this growth occurs in South America and Africa as well as in the countries of the former Soviet Union, especially Russia. More Mormons live outside the United States than inside it by the late 1990s.
Currently, South America is seen as the primary growth market for the LDS Church.
The laws passed by Utah gives a state controlled by a political hegemony the ability to define desirable and undesirable immigrants. The law will be administered by a political machine that is very much interested in maintaining its rock solid voting block.
As an outsider in Utah, I see the law as a negative development.
This game of trying to influence population by immigration is not unique to Mormonism. The history of Cyprus shows a conflict in which Greek and Turkish groups vied for control of a Mediterranean island.
When I lived in the Bay Area, progressive professors lectured on plans to use immigration to maintain progressive hegemony in California.
IMHO, the worst possible outcome of the immigration debate is to create a system of local controlled immigration as local groups seeking political influence will manipulate immigration for political power.
Utah is not showing a positive path forward in the immigration debate. Creating a system that allows local authorities to deport those who they find undesirable rewarding those that follow the lead of the local political block will end up creating an oppressive society.