I am not aware of a rule that says you have to play through when invited. However, in most cases, it’s best for you, and the players behind you, to play through. If you decline and continue to wait for the slower group in front, groups behind you are going to be held up by the slow play, too. The best move for you is to play through and work toward being comfortable playing in front of others.
Your feelings of nervousness are being created by your thoughts about the situation. I imagine when you are invited to play through, your thoughts move away from your game and into what other people may think of you if you hit a bad shot.
One of my favorite thoughts to use in these anxious moments is, “What other people think of me is none of my business.” It’s none of my business because we can never know what another person is actually thinking, and we cannot control other people’s thoughts. Your nervousness comes from your mind making up thoughts about what other players will think if you hit a bad shot. For example, your mind will create thoughts such as, “She should be embarrassed. She’s a terrible golfer. We shouldn’t have let them play through if she’s going to play like that. She’s stupid.”
Trying to pre-determine someone’s else’s thoughts, and mentally reacting to them ahead of time, is mental gymnastics and a waste of your mental energy and talent. Even if you hit a fantastic shot, they could still be thinking something negative. However, if you hit a good shot, their thoughts do not bother you because you do not feel insecure about what you think they are thinking.
Whether you hit a good shot or bad shot, it’s the same circumstance. People may be watching and having thoughts, but you cannot know what they are. The only thoughts that can upset you are your own thoughts about what you think other people might be thinking. You cannot control their thoughts, but you can learn to manage yours.
When you become aware of the nervous feelings, I offer you take two deep breaths as a trigger to come back into your own mind and out of theirs. Get ready for your next shot and begin focusing on the steps of your routine.
My guess is that when other players invite you to play through, they are thinking more about themselves and their golf etiquette, than about you personally. They know they are playing slower than you and are trying to do the right thing by standing aside.
If you do hit a bad shot, golfers watching are likely thinking, “I’ve been there.” However, that’s only speculation. Who knows what they be might be thinking? It is not of your concern. Focus on your next shot, just as you would if no one was watching.
When you learn to manage your thoughts on the golf course, you learn to manage your thoughts for life.