The problem with chlorine and black hair is when someone has a chemical relaxer. The chemicals in the relaxer and chlorine clash, and could cause breakage if the chlorine is not removed.
Unrelaxed hair also needs the chlorine removed, but it is not as urgent, as far as I know. The chlorine will build up in the natural hair and be gunky, etc., so you must rinse your hair thoroughly when you swim.
I have tried chlorine remover shampoo, and I think it stripped my hair and made it more vulnerable to breakage when I had a relaxer. The best thing for me was to wash with my regular shampoo and then condition it.
One way to protect black hair from chlorine etc is to wear braid extensions. That's a short-term solution, at least.