In a diverse society the Catholic narrative, of course, is one among many, and cannot demand special privileges. Nor does it seek to. But it does seek expression, not just in newspaper columns or on airwaves, but in schools, charities, and homes for the elderly; and it asks for the right for these organisations to witness to the beliefs which drive and inspire those who run them and work for them, even when these appear to contradict contemporary mores.
An authentically pluralist society allows for this diversity – and the state encourages and protects it, balancing the various rights involved. To take a recent example, Catholic adoption agencies should have the right not to consider same-sex couples as adoptive parents if they believe (because of what they understand to be God's vision for humanity) that the man-woman binary model is in the best interests of children.