I think there may be a bit of anachronism here although I am not entirely sure. Bryan ran for president in '96, '00 and '08 with national debut "Cross of Gold" speech catapulting him into prominence in 1896 much as Humphrey, Reagan, and Obama would later be sent into orbit (Reagan literally) by their national debuts. The Scopes trial was in 1925, and Bryan had started to vehemently attack Darwinism after WWI. He had spoken out against it earlier as well, but after his initial run.Bryan was not a young earth creationist and not really one in the modern sense. And it was not really uncommon to reject Darwinism at the turn of the century. Indeed, most scientists did. They didn't reject evolution, but they did reject Darwinism, primarily because a workable theory of heredity was lacking. This was rectified from 1900-1918 from the rediscovery of Mendel to Fisher's crucial paper integrating Mendelism and Darwinism. But it really should be emphasized that many major scientists rejected Darwinism before 1900. Now they probably rejected it for different reasons from Bryan, but the Darwinian mechanism of evolution certainly wasn't a settled fact at the time. Did Bryan have contempt for the evidence at the time that he ran (which is when you could have voted for him)? Very unclear. How far was he willing to integrate evidence into his biblical worldview? I don't really know, but at least one historian (Ronald Numbers) claims that he was willing to accept a geologically old earth and read 7 days figuratively.So while it is true that at the end of his life (or a few days before the end) he rejected Darwinism because he was very worried that the mechanism of natural selection (espcially as seen through the light of Social Darwinism) led to the moral decay he saw in WWI, he may not have held that view 3 decades before and certainly the science wasn't settled at that time.
Of course, current politicians have no such excuses.