Personally, I think it's a bit rude.
I would never dream of asking someone to move while I compete. I should be prepared for anything... If I'm not, then it's just not my day to place. There will always be another show.
A barn where I boarded Gator had stands where people could audit lessons/rides/clinics etcetera at the outdoor arena. I was riding one day, and a woman was sitting on the stands. It was a chilly day, and she had a pink blanket. Apparently she couldn't get comfortable, as she kept standing and fiddling with the blanket, even shaking it out.
Gator had a FIT. He was terrified of the thing. He gave a nice spook and spin at top speed--somehow I managed to keep my seat xD This happened three times (each time I passed her) before she asked if she was scaring him, and should she move. I told her no, that she was fine and Gator was just being silly. I thought it would be rude to make such a request.
Piggybacking off of that, I took my three year old filly to a rather large 4H show a couple years ago. This was her first show, and I had planned to just take her for exposure and not enter.
She did so well, and I had brought my clothes just in case, that I ended up entering her in a simple walk-trot class. The judge requested that everyone in the stands be quiet, as she was a baby and still figuring everything out. I didn't request it. If the judge/announcer chooses to ask someone to move then fine. It's their show. But I certainly wouldn't.
The sensitivity of the internet baffles me.