Skin colour must not determine admission.

The key is “therefore” in the question.

The question does not describe sold-out admission or a safety rule applying to everyone. It identifies skin colour as the reason for refusal. That link between a personal characteristic and less favourable treatment makes the discrimination apparent.

Article 3 of the Basic Law subjects state action to equality and protection against discrimination. The General Equal Treatment Act also provides protection for services offered under civil law. “Open to the public” and “operated by the state” are different: a privately operated pool can also offer its services to the public.

The other three answers

All four terms describe rights, but only one identifies the exclusion described.

Objective rules must not disguise exclusion.

A pool may have lawful admission and safety conditions. That does not permit refusing people because of their skin colour. Even a seemingly neutral rule can be legally problematic if it particularly disadvantages protected groups without objective justification.

An actual dispute depends on the precise circumstances and applicable procedures. The clear exam answer does not promise a particular amount of compensation. It identifies the principle violated: equal treatment.