"What if?" questions are notoriously difficult to answer. They are also fascinating, as they provide fuel for discussions about history. The events of the 1876 disputed election had two primary causes.
First, the Electoral College distorted the outcome. Samuel Tilden, the Democratic nominee, won the popular vote. He garnered about 250,000 more votes than his primary opponent, Rutherford B. Hayes. This distortion of the popular vote has occurred on a number of occasions—most recently in 2000 and 2016. The reason for this is that the Electoral College was never intended to operate alongside a popular vote. It was supposed to operate in an electoral environment where there was no popular vote. Also, in 1876, the election returns were disputed because two sets of returns were turned in by three states.
Second, the North and South had grown tired of Reconstruction (1865–1877). By 1876, only Florida, South Carolina, and Louisiana remained under Republican control. Therefore, Reconstruction was practically over in any case, so the ignominious results probably just hastened its end by a few years. Hayes won the White House by agreeing to withdraw Northern troops from the three remaining Southern states, and he carried this out in 1877. Had the Democrats won in 1876, the final end of Reconstruction would have been just somewhat more gradual.