Mormons wanted Utah to become a state. Their practice of polygamy made the rest of America resistant to that idea. Polygamy had to end for Utah to become a state.
When LDS President Woodruff found a way to end polygamy, he had to both show Mormon willingness to be good, law-abiding Americans and show respect for early church revelations that had made polygamy one of their defining practices. Even while ending polygamy, he didn't want to show disrespect for earlier teachings of church founders, particularly of the prophet Joseph Smith and his immediate successor Brigham Young.
So Woodruff wrote the following in what is - like the Pope's official pronouncements in the Catholic Church - considered to be as binding as scripture.
"nothing in my teachings to the Church or in those of my associates,during the time specified ... can be reasonably construed to inculcate or encourage polygamy," and so church members should follow his example in submitting to the law. He concluded, "I now publicly declare that my advice to the Latter-day Saints is to refrain from contracting any marriage forbidden by the law of the land."
By not explicitly refuting early church teachings, Woodruff's carefully worded revelation essentially turned over the definition of marriage to the state. It is a curious situation, essentially subcontracting the definition of marriage to the government. And in that context, it makes sense that they'd be so eager to resist a change in the law on which their reliant. Because of this, Mormons aren't just ordinary political activists; they're protecting their church teachings.