By that logic, surely we can't feel anxiety about anything.
And for sighted people who get tongue-tied in the presence of someone famous, I would submit that it only eases if they turn or look away because they rely more on their sense of sight than they might perhaps realise.
I'm a naturally calm and down-to-earth person but I've met several blind people who ... er ... are not. I can't imagine they would restrain themselves in that sort of situation just because of a lack of visual stimulus which, you should of course remember, is not a lack in many cases because they were born without or have adapted to its loss.

I'm sure some blind people would be unable to speak if they met an idol.

Oh I’d run in terror. That is if I could even recognize a celebrity because I don’t know any of them lol

! I've met many famous people from multimillionaire business people to high-ranking politicians and I do get star-struck especially when my Dad tells me how important that person is.

To answer your question, Yes, we do. Met Amal Clooney and Gordon Ramsay and both times, I was starstruck.

I have totally been star struck and I'm totally blind. I met Weird Al Yankovic at Amoeba Records in LA, and I heard his unmistakable voice and I freaked out. I did get a nicepic with him and even gave him a business card for a podcast I was doing at the time. Very nice guy.

Why wouldn’t a blind person be starstruck this isn’t just a sighted person thing you don’t need eyes for that haha!