William Jennings Bryan was a populist radical, not a conservative
One of the myths that grew out of the Scopes trial was that William Jennings Bryan was an arch-conservative religious fanatic, and a stand-in for today's "Christian Right." The trial is framed as a conflict between secular liberalism (represented by Darrow) and ultra-conservative fundamentalism (represented by Bryan).
The reality is more complicated. William Jennings Bryan was NOT a conservative. He was a populist radical who opposed the Gold Standard, supported the progressive income tax and universal suffrage, and promoted social welfare programs for the rural poor. He'd be considered a socialist by today's standards - probably to the Left of most liberal Democrats on economic issues. True, he was a creationist (albeit an Old-Earth creationist, not a literalist young-Earther), but his main opposition to Darwinism wasn't religious but political: he knew of "Darwinism" primarily as an ideological justification for laissez-faire capitalism and robber baronism.
If anyone during the Scopes trial represented views that are considered right-wing today, it was journalist H.L. Mencken (E.K. Hornbeck in the fictionalized version), an economic libertarian who opposed the welfare state and Roosevelt's New Deal and an admirer of Nietzsche and Herbert Spencer.
The only reason Bryan is retrospectively perceived as a "conservative" is that we now associate religious belief with "the right" and secularism with "the left," this wasn't always the case. The fact is, the political spectrum back then made more sense: the rural poor supported religion and social welfare, the middle and upper classes had less use for either.