I disagree with your view that morality is subjective. Your assumption is that either truth (the basis for morals) is relative or it is unknowable. Truth by definition is absolute and objective. Logically then an assertion that claims to be true, when applied to itself, should also be non-contradictory. While we shouldn't impose our morals on others we should debate the truthfulness of our morals (the sum total of our beliefs). If this enquiry proves false then we need to reevaluate our beliefs. The statement, "Morals are subjective" is an absolute statement when applied to itself implies a "subjective absolute". This does not make sense. You can not therefore know WITH absolute knowledge that morals are subjective. However I believe that Morals are and should be objective. Question is how does one get to "know" these morals. The answer precludes a necessity for a moral lawgiver. The morals prescribed by this moral lawgiver have to be non-contradictory. On the basis of a non-contradictory test, one can reject different moral standards. No one can force someone to stop believing in contradictory morals. ie. live a lie! For more on this google "Law of non-contradiction
