Yes, pretty much every conceivable ideology in the US [0] has its own party (or more than one!) distinct from the two major parties for those adherents who don’t understand the futility of third parties under normal circumstances in the US electoral system, or who care more about ideological purity of association than acheiving policy goals through the political system, or who think that we are on the edge of a party shift where their preferred party could plausibly replace one of the two major parties (its happened twice before in US history, your party could be next!).
That doesn’t mean that many of those ideological factions that have their own parties don’t also have substantial (often, much larger) number of adherents within one, the other, or sometimes both of the major parties.
[0] For instance, a non-exhaustive list for the other factions I’ve identified as substantial Republican constituencies:
(1) Social/religious conservatives: Christian Liberty Party, Constitution Party
(3) corporate neoliberal capitalist: Unity Party, Moderate Party of Rhode Island
(4) American nationalist: Constitution Party
(5) White supremacist/nationalist: American Freedom Party, American Nazi Party
