I suggest make equal relation completely separate concept.
Instead of equals(Object) method use static method boolean equals(TypeFoo, TypeFoo) for each type you want to compare.
If you have TypeBar inherited from TypeBar you just get another method.
If you have some algorithm that requires checking equality relation just parametrize it with interface EqualityRelation<T>{ boolean equal(T, T);} and pass relation you want to use.
No surprises here. You always explicitly tell which relation you want. You can have as many relation between same type as you want. Want to use color and x coordinate of your ColoredPoint? No problem: just define new relation, it is just a method.