School.java

public class School {
    private final String name;
    private final String nickname;

    public School(String name, String nickname) {
        this.name = name;
        this.nickname = nickname;
    }

    @Override
    public int hashCode() {
        return 1;
    }

    @Override
    public boolean equals(Object obj) {
        return (name.equals(((School) obj).name) || (nickname.equals(((School) obj).nickname)));
    }
}

You wrote:

Null safety and typechecking ommitted for clarity

Reproducing that here because I'd forgotten by the time I read the code.

return this.class.hashCode();

would be more efficient in heterogenous collections.