My thought is, dogs in the ring should be trained to handle whatever is going on outside the ring. No excuses. If you are there, your dog should be ready. And a clicker isn't that big of a deal, as far as noise goes. If a dog at a trial can't handle hearing a clicker there, it doesn't need to be there. So, go ahead and use it to train a better response with Koji.
I think a lot depends on how high drive your dog is, and how observant they are. Starr is mid drive. He's also a young, intact male, and he's incredibly observant. He'll run past turkey with no hesitation, but last weekend, a competitor walked their female dog who is close to being in season within 5 - 10 feet of the ropes as we were doing the dog walk (which was right on the ropes). Starr jumped off the dogwalk, went through the ropes, and checked her out. As soon as I called him he returned to the ring. The next day, as we were doing the weaves on a chances run (again, beside the ropes), a competitor with one arm walked past him. Starr didn't leave the ring, but he was so focused on her he couldn't complete the weave poles. He's a ridiculously observant dog - he notices when my neighbours move their garbage can a foot, and he's never met a person without an arm before, so he fixated on her (didn't leave the ring, but stared at her and couldn't focus enough to do the weaves). The woman very graciously met him afterwards and gave him treats so all is good.
The clicker isn't a big deal, but having a reactive dog near competing dogs is. If Starr hears a clicker while he's running the course, he'll ignore it. A reactive dog, however, will get a reaction from him if it's within a certain distance. He has an excellent recall - most dogs don't When you're working with reactive dogs, you always have to look at worst case scenario - if the dog escalates, what could potentially happen? And how many competitors have a reliable recall on their dogs? You could unintentionally end up with a dog fight, which would make the situation even worse for the dog who is reactive.
I can't speak for others... and I have a feeling most coming from obedience/rally are similar to the hunter/jumper people who give you a dirty look if you make a bunch of noise because their horses aren't trained to deal with it but I at least wouldn't be bothered by it.
I think it's just common courtesy. Everyone who is competing in agility/obedience/rally/freestyle has spent thousands of hours and a lot of money. Why would I want to sabotage them? I think everyone deserves the best chance possible to succeed, so I won't leave treats around the ring, I keep a wide berth of the ropes, I never use squeaky toys or balls, I tug a respectful distance away, I avoid eye contact with competing dogs when I'm bar setting, etc. None of these things will distract my dog, but I would feel horrible if they distracted someone else's dog.