My local council pool run classes for disabled children and a group specifically for ASD. Have not tried it yet (DS is just 5), and they have 10 in class which put me off, although 4 helpers in pool. At least they are trying.
Social services may fund extra support / 1:1 lessons via short breaks.
Our ABA team often accompany their children to swim lessons and in effect 'translate' between the instructor and the child, and obviously are adept at keeping the child on task.
You need to find a way of importing how your child learns eg use symbols, written instructions, 1:1 imitation into the pool. Can your child learn from group instructions outside the pool? If not then its probably unrealistic for him to do it in such a noisy environment
I think it is probably an issue of the teachers not knowing how to teach your DS and expecting him to learn in the same way, when clearly he doesn't.
My older boys have lessons (4 in a class) and when I have raised DS3 (ASD) with the lady who runs the company she said that only 1 or 2 of her instructors would teach kids with ASD, dyspraxia etc etc as the others felt that they didn't know how and felt bad when the child did not make progress and wrong for taking the money. I actually felt that at least they were honest, although a bit down she was putting me off. I would rather they acknowledged their lack of ability to teach than blamed my child for not listening! She was willing to give it a go if we got our ABA team to be involved / do some training.
I would probably start again with a new instructor as this one does not seem very inclusive, perhaps find a small class (many private ones are 4 children only). But perhaps approach it more systematically eg that they give specific 1:1 instructions perhaps simply saying 'copy me' and demonstrating, explain how to get your child's attention, use rewards, perhaps use laminated symbols or a visual schedule. Whatever works outside the pool. Perhaps you could do a 1:1 lesson first to train up the teacher first?
Your council should have an inclusion leisure person who can help and maybe provide training or support so your child can be included.
If you have a council pool then you can probably insist they make reasonable adjustments.