Earlier quoted context omitted.
You have your history all wrong. If you try to squeeze the Republican party of 1900's economic policy into the current American liberalism vs. conservatism spectrum (I say squeeze because obviously the political positions of that time were different than today's), they would be liberal, and the Democrats of that time would be conservative. So the fact that once upon a time red meant liberal, but no longer does, does…
If you pay any attention to current political discussion, e.g. the field of Republican candidates they do NOT argue in favor of inequality. They describe it as a problem just as the Democrats do. And of course that's false. The Democrats of the 1900s are conservative; the new deal is the most iconic conservative movement we've ever seen yes? And Hoovervilles were created by socialist thought?
Virtually no Republicans have a stated goal or platform of reducing economic inequality. Pretty much every Democrat running for president does. To claim otherwise is also clearly untrue.
I suspect you are mixing up the fact that in American politics, conservatism (which is "red") consists of what Europeans would call liberalism (in fact the New Deal was part of the reason the definitions flipped: https://en.wikipedia.org/wiki/Conservative_coalition).