I would think the last thing you'd want is tune everyone out. It a busy show warmup ring, you need to be paying attention to where everyone is. The are rules of the road in place to keep everyone safe and avoiding collisions. You should always ride left to left and call out every warmup fence you intend to jump. You can't do those things if you "tune out" and don't know where anyone is relative to your horse.
Honestly, if you are that worried about people watching you, why are you even showing? That's kind of what happens at shows. Ideally you should practice your jumping in front of as many people as possible so you get used to it and it ceases to have an effect on you. Just concentrate you what you and your horse are there for and try to have fun.