In short, because they founded the state.

The Mormon domination of Utah came to be as they were the first whites to permanently settle in the territory, known as the “Mormon Exodus”, many thousands of them fled persecution which included a brief war, the 1838 Mormon War.

After the assassination of the Church of Latter-day Saints’ (LDS) founder, Joseph Smith, Mormons faced increasing hostility in Nauvoo, Illinois where they presently resided. Mormons were blamed for the failure of banks and seen as having all the wealth and power in society due to their insular nature, I suppose you could say it is comparable to the belief modern anti-semites hold about Jews controlling the media

The new LDS leader, Brigham Young, led the community 1,300 miles from Illinois to present day Utah to settle the Great Salt Basin, to form a new community where they would be free from persecution. Known as the Mormon Pioneers, after a long trek, and including European converts in their number, totalling approximately 70,000, they arrived in the Great Salt Lake Valley on July 22, 1847. This settlement would become the present-day Salt Lake City.

The community struggled at first and almost led to famine,

“meager gardens planted in such haste in late July-potatoes, buckwheat, and turnips, with some corn in tassel-lasted only "until the first company [of immigrants] came in and turned their catde loose; they devoured crops that would have been ready to harvest in a few days," anguished

John Steele.” (Schindler, p. 32)

However, grain recovered and a “miracle” of insects and birds came which helped the crops flourish, and the settlement expanded rapidly. An influx of converts and continued prosperity increased calls for statehood, yet this proved to be more difficult for Utah than for other Western territories.

Campaigns for Statehood began shortly after the arrival in the Great Salt Basin. The settlers organised the state as “Deseret” and requested its admission to the Union. Yet, the federal government did not want to give Mormons their own state, and be held to ransom by them, so they made “The Compromise of 1850”, relegating the settled area to a territory named Utah. The main obstacle to a Mormon state was polygamy, taboo to other Christian denominations.

Requests for statehood continued, yet both Democrats and Republicans were fearful of Mormon political influence in Congress, as they would negate the influence of Democrats and Republicans in Congress with elected officials from their own parties joining the electoral ranks. Indeed, perceived Mormon influence in the political sphere one such thing they had been persecuted for in Nauvoo, leading to the initial exodus. Utah was finally admitted to the Union in 1896, after a compromise on marriage had been reached and local Mormon politics had been aligned with the major national parties. Mormon politics became secularised, Utah joined the Union.

However, as your question states, heavy religious influence continues to pervade many aspects of Utah’s state laws. One good example is the strict alcohol laws in bars and restaurants, with “Zion curtains” separating bartenders preparing drinks containing alcohol from customers who order them. These laws were reformed in 2017 however, and this is no longer required.

Whether laws should be secular or the extent to which religion can influence legislation is probably a question for a political scientist, but it can be argued that many laws around the world have a basis in religion, whatever it may be, and thus it can seek to regulate the morality of a society.

​

Bibliography:

William Mulder, "Mormonism's "Gathering": An American Doctrine with a Difference, Church History, Vol. 23, No. 3 (Sep., 1954), pp. 248-264)

Klaus J. Hansen "Political Deliverance: The Mormon Quest for Utah Statehood Leonard J. Arrington by Edward Leo Lyman"
The American Historical Review, Vol. 93, No. 4 (Oct 1988)

Harold Schindler "Great Salt Lake Valley, “The Place”: First Few Years in “Deseret” Test Pioneers’ Mettle, 1847–1850" from In Another Time (University Press of Colorado, Utah State University Press. 1998)
Melvyn Hammarberg, "A Sampling Design for Mormon Utah, 1880"
The Journal of Interdisciplinary History, Vol. 7, No. 3 (Winter, 1977), pp. 453-476

David R. Jr. Williams, In Defense of the Secular Purpose Status Quo, 102 Va. L. Rev. 2075 (2016)

Thank you!