Grayden correctly points out that if you don’t care then it’s possible.
But (there’s always a but).
It’s my experience not many can play without caring. I can only think of one golfer who is able to do it consistently. He plays for fun and doesn’t care what scores he shoots. His scores are inconsistent but it doesn’t matter – he has a ball and it’s an experience to play with him.
For everyone else you’ll need a strategy. When the scorecard is in your pocket and there’s eyeballs staring you down, you need a coping mechanism.
Breathing and relaxing helps. So does having a clear goal with each shot.
But nothing calms the mind and eradicates the fear like acceptance.
Accept that the fear/self-doubt/nerves are normal. Then keep playing. When you can mentally accept the odd bad shot and realise it’s not the end of the world, fear will have very little control on you. When you can truly accept that it’s just a silly game and nothing bad can happen then maybe you’ll reach a level where you can “care without caring”.