Maybe Bryan would have had a chance in 1900 if he had indeed made the election a referendum on anti-imperialism. To quote an old soc.history.what-if post of mine:
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We have had much more here on the possibility of Bryan winning in 1896 than in 1900. This is understandable, because McKinley won even more decisively in 1900 than in 1896:
http://psephos.adam-carr.net/countries/u/usa/pres/1896.txt
http://psephos.adam-carr.net/countries/u/usa/pres/1900.txt
However, was this inevitable? It seems to me that Bryan's biggest mistake in 1900 was sticking with free silver, even though he insisted that imperialism was the "paramount issue" of the campaign:
"Bryan's determination [in 1900] to 'stand just where I stood' on the silver issue in 1896 cost dearly. Most Americans agreed with the editor of the Republican *New York Press* who replied to this statement, 'Sit down, Mr. Bryan. You must be awfully tired, too.' In 1896 Bryan had argued that only increased amounts of money could restore prosperity, but when prosperity arrived with an influx of gold in 1897-1900, he never could bring himself to drop that issue and discuss relevant subjects. By 1898 world gold production was double that of 1890; silver, on the other hand, had suffered a relative decline in production. The statistics and the prosperity were there for all to see, but the Nebraskan refused to recognize the message of the production tables. As Thomas B. Reed remarked in 1900, 'Bryan had rather be wrong than president.' Not until 1907 would he admit that free silver was no longer a political issue..." Walter LaFeber, "The Election of 1900," p. 1911, in Arthur M. Schlesinger, Jr., Fred L. Israel, and William P. Hansen (eds.), *History of American Presidential Elections, 1789-1968, Vol. III.*
Bryan would not have to acknowledge that he had been wrong to support free silver in the past--merely that new conditions had rendered it obsolete as a panacea. Suppose he had so acknowledged, and run his campaign entirely on other issues, above all anti-imperialism (but also some domestic issues, such as the trusts)? Even in OTL he got the support of some Cleveland Democrats on the anti-imperialism issue, but Cleveland himself and many others refused to back him, saying that free silver was still the paramount issue. Also, free silver was at least one of the reasons why Bryan failed to get the support of many anti-imperialist Republicans. Benjamin Harrison, though opposed to the annexation of the Philippines, finally yielded to pressure and in October came out against Bryan (though not saying anything good about McKinley), which hurt the Democrats in Indiana. George Frisbie Hoar of Massachusetts who had led the fight in the Senate against the Paris Treaty, sided with McKinley, arguing "that the free coinage of silver at 16 to 1 means national dishonor, great injury to business, the reduction by half of all savings, the destruction of the standard of value making all business transactions gambling transactions, and a great reduction, not only of the savings of the wage-earner, but of the wages he is to earn hereafter. Now, can Mr. Bryan put us on a silver basis, and will he? He says he will, and he says he can." Hoar also questioned the sincerity of Bryan's anti-imperialism in view of the Democratic Party's widespread racism:
"[The Republican Party] has made, in my judgment, one great mistake. But with these two parties standing side by side, promising justice and good government to this Oriental people, I trust the party that has made but one mistake, rather than the party whose sole existence has been a mistake. I prefer the Government which the Republican party has established at home, to the Governments which the Democratic party has established and has sought to establish at home. I prefer freedom and justice and equality and local self-government after the pattern of New England and Massachusetts, rather than after the pattern of Mississippi and South Carolina. I like the gospel according to McKinley better than the gospel according to Bryan. I do not believe that Mr. Bryan or his associates will do better for ten million people of another race in the Philippine Islands than they have done and mean to do for ten million American citizens in the United States."
http://www.humanitiesweb.org/human.php?s=s&p=l&a=c&ID=1095&o=
Such prominent anti-imperialists as Andrew Carnegie announced that they could not vote for Bryan in view of his positions on issues like free silver, the Supreme Court, and the income tax. Carl Schurz did vote for Bryan but complained afterwards that it was the most distasteful thing he had ever done.
Free silver also hurt Bryan among German-Americans, who knew that Germany had demonetized silver back in 1871 (two years before the US) and associated free silver with a "dishonest dollar." "The influential New York *Staats Zeitung* announced in mid-October that it was endorsing McKinley because, although it disliked imperialism, it found Bryan's passion for silver more objectionable." LaFeber, p. 1910.
Even with the albatross of free silver, Bryan did make gains in some eastern states on the anti-imperialism issue; New York went from 57.6-38.7 percent for McKinley in 1896 to 53.1-43.8 for McKinley in 1900. No doubt, without free silver Bryan could have narrowed the margin still more, though whether he could have actually won the state is doubtful given the unpopularity of Tammany's Boss Croker; Bryan in his Cooper Union speech of October 13 impulsively and unwisely held his hand over Croker's head and intoned, "Great is Tammany and Croker is its prophet!" (Croker had famously declared of the free-silver issue, "I'm in favor of all kinds of money--the more the better.")
Moreover, free silver does not even seem to have helped Bryan in the West (where indeed he lost a number of states he carried in 1896). I suppose it it possible that if Bryan had abandoned free silver, diehard Populists and Silverites would have run a third party ticket against him in 1900, but I doubt that it would get many votes, and the very fact of such a ticket's existence might have helped to reassure conservative Democrats and Independents ("Mugwumps") that Bryan wasn't so radical.
I would not go so far as to say that Bryan would actually have won in 1900 had he dropped free silver--the country, after all, was prosperous, and perhaps those observers who said that the voters just weren't that concerned about imperialism were correct--but presumably Mark Hanna knew what he was doing when he chose it as his major issue against Bryan: On opening Republican headquarters in Chicago in September, he pointedly said, "I contend that the main issue in this campaign is free silver, and every collateral issue that has been injected in this campaign has been for the purpose of throwing dust in the eyes of our working people." LaFeber, p. 1896.