How to play against the blacklist rival?

I don't understand the question.

If you want to play against a blcklisted player, tough. they're blacklisted and can't play online.

Have you used a trainer/ crack programme of some sort?
Some trainers give you all achievements unlocked, all cars availalbe, unlimited cash, etc. If you've used such a trainer, your save game profile becomes modified accordingly. In short, unless you quit the trainer, you're gonna have to restart the career.