The Republican Party was founded on the principles of classical liberalism and in opposition to the institution of slavery, and it remained that way for at least the first 20 years of its existence.
The Republican Party was founded on opposition to slavery sure, but not on the principles of Classical Liberalism. Indeed, besides the issue of slavery, it wasn't really founded on much at all. This is why the early Republicans had Jeffersonians like Hannibal Hamlin and John C. Fremont in the same party as Whigs like Abraham Lincoln and John McLean. To my understanding, it wasn't until after the war that the Republicans came into their own ideologically as a Conservative party.
Even when the Radical roots of the party were betrayed in 1876, the Democrats weren't obviously more left or pro-working class. Pre-Bryan, I don't see them advocating for labor reform or antimonopolism any more than the Republicans.
If you wanted to make the arguments the Democrats were not more any more anti-monopoly than the Republicans you shouldn't have brought up their opposition to tariffs a few posts beforehand.
Post-Bryan, both parties advocated for those policies in varying degrees, Bryan more so than his Republican opponents and Roosevelt more so than his Democratic ones, and Wilson and Hughes about the same.
It is true that after Bryan showed up both parties adopted these policies to greater degrees, but that wasn't due to Bryan, it was because the entire nation recognized that the monopolies and big trusts had grown too large and powerful. Even then, there was quite a bit of disagreement over what exactly was to be done (consider how Teddy Roosevelt always went to pains to distinguish between good trusts and bad trusts or how he always focused on those trusts which broke the law as opposed to condemning the entire system ala Bryan or Wilson). Speaking of, when you say that Wilson and Hughes were both opposed to monopoly about the same, that's just not true. If you don't believe me, consider the "Business" section of the 1916 Republican Platform
The Republican party has long believed in the rigid supervision and strict regulation of the transportation and of the great corporations of the country. It has put its creed into its deeds, and all really effective laws regulating the railroads and the great industrial corporations are the work of Republican Congresses and Presidents. For this policy of regulation and supervision the Democrats, in a stumbling and piecemeal way, are within the sphere of private enterprise and in direct competition with its own citizens, a policy which is sure to result in waste, great expense to the taxpayer and in an inferior product.
The Republican party firmly believes that all who violate the laws in regulation of business, should be individually punished. But prosecution is very different from persecution, and business success, no matter how honestly attained, is apparently regarded by the Democratic party as in itself a crime. Such doctrines and beliefs choke enterprise and stifle prosperity. The Republican party believes in encouraging American business as it believes in and will seek to advance all American interests.
I get the sense that the "Democracy" of the Gilded Age was a plutocratic political machine that relied on corruption, intimidation, and voter suppression to win elections for power's sake. Not altogether unlike today's Republicans.
Sure, but that doesn't mean it was lacking in ideology. You yourself compare the lust for power in the gilded age to the present Republican Party, but would you deny that they are an ideological party?
