The discussion of politics has brought to the surface many strange exhibitions of feeling among members of the Church. Such exhibitions would have been deemed incredible a short time ago. Many have yielded to a spirit that produces anything but harmony and love, and there is considerable danger that this agitation may almost prove too strong an ordeal for the faith of many. . . .Well. . . apparently not much has changed. The whole quote is at Keepapitchinin which I heartily recommend.
The context in 1892 was that Utah was preparing for statehood (as it had been for about 40 years). It took Utah a long time to become a state for a lot of reasons which we won't go into now, but one of them was the concern of the US Congress about the LDS Church's influence in politics. In territorial days a two-party system developed in Utah but it wasn't with the traditional, national parties. The Liberal Party was made up of the non-Mormons and the People's Party was the Mormon Party. Leaders of the LDS church wanted to see a broader diversity of political activity to avoid any claims that the church controlled politics, so they "assigned" members of the church in Utah to be either Republicans or Democrats (That is so funny on so many levels, yet the only practical thing they could have done!) The Utah non-Mormons more naturally divided along the national party lines as their "Liberal" party became irrelevant. I suppose a cynic could say that the church still wanted to control politics in both mainstream parties, but for a hundred years after, Utah was a swing state electing Mormons and those of other faiths and a pretty fair balance of Democrats and Republicans to local and national offices reflecting national trends.
The church does . . . Expect its members to engage in the political process in an informed and civil manner, respecting the fact that members of the Church come from a variety of backgrounds and experiences and may have differences of opinion in partisan political matters. From Official Statement on Political Neutrality.During the last presidential election year, the First Presidency issued a letter to members of the LDS Church in Utah to encourage them to participate in their local political party caucuses:
Principles compatible with the gospel may be found in the platforms of various political parties. We encourage members to attend their precinct caucus meetings. From First Presidency Letter on Utah Political Caucuses, March 2010.