Speaking as a Mormon myself...
Giving up polygamy was crucial for the Church. By 1899 in OTL it was dangerously near bankruptcy, and held $2 million in debt. Federal confiscation of LDS Church property, as part of its campaign against polygamy, was driving the Church into a financial hole that it would not emerge from until the late 1960s. Worse, the U.S. government threatened to confiscate even religious buildings, cemetaries, and the LDS Temples the Mormons had spent so much time and money to build. Moreover, U.S. confiscation of the LDS Temples would ruin the Church, as revelation had been given that they would not fall, that they would not be destroyed. It would be a hammer blow against the morale of the membership.
In fact, President Woodruff was very smart to issue the 1890 Manifesto. It saved the Church. No doubt the LDS Church would still be around in 1898, when he died, but that extra eight years of federal oppression, compounded the the depression in the country, would have been a horrible trial for the membership. In September 1898, Wilford Woodruff would have died, and the leadership of the LDS Church would pass on to the Quorum of the Twelve Apostles and shortly thereafter to the next Apostle in line, Lorenzo Snow.
Lorenzo Snow was known for focusing on relieving the financial strain on the Church by pushing tithing reform, historically his biggest impact on the Church. He was an activist, and though a noted polygamist (as was Woodruff), no doubt he would have issued an anti-polygamy Manifesto soon after becoming Prophet, Seer and Revelator. Nevertheless, the last eight years of divergence would leave the Church in a weaker position than OTL, certainly, though those who remained would no doubt be the most zealous and learn from their experiences of self-sacrifice and whatnot. In that case, you might just have some kind of 'Reformation', as seen in the 1850s, maybe during the early 1900s. A lot of interesting things could occur, with the leadership in more zealous hands.
Utah becomes a state in 1905. Its three electoral college votes aren't missed in any of the three elections ITTL that it would have participated in OTL. It also keeps the position as 45th state accepted into the U.S.