This election was extremely controversial because many in Washington D.C. felt that Smoot's election was the LDS Church trying to control the political arena in Utah. Further controversy arose due to the continued practice of polygamy, even after the LDS church stated that they discontinued it (while I understand that this can be a contentious point for several people. This is at least what the book argues). Many in D.C. felt that Smoot may himself be a polygamist in addition to hostilities between Mormons and Protestants. This resulted in several members of the Senate refusubg to seat him. A huge trial commenced, called the Reed Smoot Hearings, which I believe has the largest collection in the US Library of Congress of trial evidence of any trial in US history. It was a big deal (and is a really interesting read). Here is a comic of the Smoot Hearings:
Courtesy of Wikipedia
Smoot was eventually seated in the Senate despite several objections from fellow senators. He ended up serving in the senate till 1933 and was a very influential and powerful member. The whole story is a very interesting, and I feel not a well know part of US and LDS history.
Smoot has a strong connection to Provo, Utah, and his house is located near downtown at 183 E. 100 S. (it is on the corner of 200 E and 100 S). Smoot lived there from 1892 until his death in 1941. The house is National Historic Landmark list; there are only 15 places in Utah that are on the list, including Ft. Douglas, Temple Square, and the Brigham Young House. It is also the only located on the list in Utah County. The list is pretty exclusive and quite an honor for the house to be there.
Here is a picture of the house at some time when Smoot was living in it (he is located on the far right in the top picture) and what it looks like today:
Courtesy of the J. Willard Marriott Library, University of Utah
The history surrounding Smoot is extremely interesting, and his legacy is a great addition to Provo. To answer the question in the title, although the LDS church does not encourage Apostles to be Senators (and I think they may have just come out and forbidden it) in the 1900's the situation was different and they did encourage an Apostle to become a Senator from Utah. I encourage anyone who has a little bit of time to read a little bit more about Reed Smoot. Below are a few additional pictures of the house:
I have to add one additional photo. I love the neighborhood surrounding the Smoot House and feel that it is one of the best in Provo. Also the orange house below was an inspiration for my sister's own house which she painted orange. I thought that I'd add a photo of those as well. Here they are: