Part of the convenience of a 2 party system (for oligarchs) is that it means you can teach people on "both sides" that the only thing that matters is beating the other "side".
What makes that really convenient is that even when people switch from one "side" to the other the logic still applies, so no matter which "side" they are on, they'll believe it's their job to support "their" candidates no matter how awful they are.