Can I bring my own towel and shampoo to the barber shop for a haircut? You won't let the boss laugh at me, will you?

Yes, it is an insistence on the quality of life, and there is nothing to laugh at.

But the boss may think that you are an insult to the things in their shop.

When you explain to your boss, you'd better use appropriate wording. Think of a reason not to let others think that you just don't like their shampoo and towels (even if you think so).