We shouldn’t run a red/blue campaign, but we shouldn’t run a blue/blue campaign either. That’s a defeatist campaign, a “if you can’t beat them, join them” campaign.
Why is it that Rudy doesn’t suffer from the “republican” backlash? Because he’s not seen as republican right now, so people will say they’d vote for him.
When Rudy is the “republican” candidate, and there is a single opposing “democrat” candidate, Rudy will lose any state that would be falling to democrats. He has no message to inspire people to come vote for him, just an aura of inevitability.