Polygamy is a rank offense against the equality principle, which is why the Republican Party in their 1856 platform denounced it along with slavery as the one of the “twin relics of barbarism.” ~John B. Kienker

Perhaps it was their deep love of equality that drove them to denounce polygamy, or perhaps it was that many Mormons had adopted strong pro-slavery views and represented a potential impediment to the spread of Red Republican “free men, free labour” ideology into the territories.  It would have had the added advantage of associating their opponents in the minds of the public with a rather scandalous marital practice.  But I’m sure it was the profoundly principled stand that was the main motivation, since the Red Republicans have always been great ones for principles.