Shultz apparently has been a Democrat in the past. But the leftward surge within the Democratic Party, especially the threat to raise taxes on the very wealthy, has forced him to move right. More or less into the realms of lassaize faire or "neoliberal" economics. Not that these aren't already rampant in both parties but they are more often publicly advocated by Republicans.
Shultz imagines he could draw voters from both parties for the win.
I imagine he would be ignored by both parties for an embarrasing and expensive trouncing.
"Be yourself; everyone else is already taken."— Oscar Wilde