Let's not mistake culture for politics. Our culture has been moving generally to what we describe as "the left" for the last 50 years. Our politics, to the right.
So I'm not sure the designations 'Republican' and 'Democrat' as used here mean much.
Biden, like Obama before him, governs as a Centrist. A Rockefeller Republican.
The 'radical' wing of the Democratic party - AOC, Sanders, et al. - is no farther left than Harry Truman was in the late 1940s.
Trump is a fascist, not a Republican. That's where the American right has led us. Sorry, but it's true.
'Republicans,' to the extent they refuse to repudiate Trump, and as we see them now in statehouses and in the House and the Senate, can also be thought of as fascists. Their agenda is not to govern, but to destroy government. They're doing exactly what Grover Norquist told us they would do. We've arrived at the 'drown it in the bathtub' part of the plan.* Again, sorry, but true.
There is no viable 'third' party.
Good luck, America.
*"My goal is to cut government in half in twenty-five years, to get it down to the size where we can drown it in the bathtub."