It's only game, you're there to have fun, your life does not depend on it. Nobody will kidnap and murder your family if you fail mechanics. The opinions of a random person about you do not matter either. Unless you're doing like half of the other players' DPS nobody will even acknowledge your name or anything. You'll just be an extra.

And if you're judged by LITERALLY EVERYONE IN THE GROUP, does it matter, really? Quit/get kicked, whatever, move on, find another group. Chances are you will never see them again, AND IF YOU SEE THEM AGAIN, they won't remember you, I guarantee it. If I actively try to think about the worst player I've raided with in the past week, I can't remember a name, or even a class.

Also, normal-mode mechanics are much more forgiving and intuitive than you probably envision them. They don't require nanosecond reaction times. If you're targeted by anything in Normal, you can probably take your time, say "Ugh", and then decide to do something about it and probably nothing serious will happen. Except for ruiner. Ruiner can ruin you pretty fast.

Tl;dr - care a little bit less about it.

But ultimately, this is about having fun. It's not a challenge you have to face in life to achieve success. If you can't stop feeling anxious about it, I assume you aren't having fun, so why bother with it at all? That's not the point of the game, just move on and do something you enjoy.