First, for the foreseeable future, there will be no element within the Republican Party that will have either sufficient interest or power to challenge the base.Compared to the Democratic Party, the Republican Party is relatively idologically coherent, though it may not look that way to participants in their intra-Party factional feuding.
Second, not until the big business elements of the Democratic Party are purged or curbed—and thus forced to fall back on the GOP as their base of power—will there be any basis for a real challenge to Trump-ism within the GOP.
But to the extent that there could be said to be a meaningful ideological conflict between Labor and Capital, that conflict largely takes place within the Democratic Party; and between corporate Democrat and Republicans, on one hand, and progressive Democrats on the other.
The Democratic factions aren't formal blocs, of course. But the basic pattern is so.