The only one that they've fully rejected in modernity is facial hair. Polygamy is partly under the rug, but still visible at the corners and by the bumps it makes. Underwear continues to shape Utah in a major way.
Brigham Young pretty much single-handedly shaped Utah, IMHO. His influence lingers to this day (in less benign ways as his "inspirational" layout of SLC streets).
Brigham Young and Joe Smith were megalomaniacs. JS wanted to be General, King, and President, and BY wanted to rule his own empire - the larger the better, which is why he sent so many people out as far as he could to settle in outlying areas.
The history I have read shows Brig wanted to control almost half the area of the western U.S. As far South as San Diego and North into Idaho and Oregon. Remember that when the mormons arrived,,Utah area was controled and belonged to Mexico. That is why Brig and the boys wanted to come here,,no goverment control.
Utah underwent three revisions of it's boundaries. The first one was huge. Taking in what is now part of Oregon California and Wyoming. This was what Brigham Young envisioned as being the State of Deseret. It even had a seaport in California near San Bernardino.
When Utah applied to become a territory congress immediately saw trouble brewing and reduced it to what is now Utah and Nevada. During the second application for statehood during the Civil War, Abraham Lincoln was a ticked off at Brigham for petitioning to enter the Union as a slave state. This angered Abraham so much that he split Utah Territory in two and made Nevada a state.
This is why the Nevada state motto is "Battle Born" and why Nevada was the only state created during the civil war. After Nevada became a state Utah's boundaries were pretty much what we have today.
I gotta correct you though, there are no sea ports near San Bernardino. The sea port BY wanted was San Diego Harbor. That's right folks, San Diego would have been part of Deseret (Utah) if BY had had his way!
to Wyoming because the feds didn't want the mormons to have control of Fort Bridger and the Oregon/California/Mormon Trail crossings over the Green River.