He doesn't identify with the Republican party, but he is a "disaffected democrat" - a group that increasingly has seen the democratic party leave them, rather than them leaving the party.

Joe may be considered right-wing by the "new democrats", who are the most vocal portions of the democratic party (the "woke" folks, even if they aren't the majority of the party currently, but they are becoming the future of the party) - this is despite Joe's views not changing much from where they were a couple decades ago. It's the party that's shifted.

It's like comedian Tim Dillon said, "I woke up one day and was asked if we should still have police and borders, and I said yes we should. Now I'm apparently a nazi." He is a comedian and this is somewhat tongue and cheek but reflects the disaffected nature and cynicism many of these folks now have for the democratic party.