they are doing this not just for moral issues. it also has to do with discouraging polygamists from settling there. there has been a long standing feud between Missouri and the FLDS (fundamentalist latter day saints) since Joseph Smith and his followers settled in the area. Joseph Smith believed that the Garden of Eden was located in Missouri and that Saints (Mormons) had the right to that land to prepare for Christ's return. This led to mob killings and a massacre of Mormons in 1838. Some fundamentalists still believe it is their duty to move to Missouri. I am fairly certain that this is not only a jab at unmarried couples, but to polygamists, who have wives that they are only "spiritually" married to.
sorry for the longwinded post. i am in the middle of reading "under the banner of heaven"