Third party candidates and their supporters sure seem to.

They don't.

There hasn't been large ideological shifts within the 2 major parties? Are you serious? I will provide you an example: look at the GOP. The past several decades right wing radicals have focused on capturing local elections and statehouses, it has been wildly successful for them and has allowed these people to completely capture the party and expel pretty much any opposition. Capturing a party is absolutely in the table, we literally have historical examples with these same parties.

Why has the GOP (and DNC) gone further right? Random radicals? No. Fascism is Capitalism in decline, it's an inevitability that the establishment parties would move towards it.