People seem to misunderstand what morality is.
Moral- from mos, moris. It means pertaining to customs or way of life. Peoples customs and ways of life include things like the kind of food that they eat, the age at which they get married, how many hours a week they work, whether they exercise, or smoke cigarette. You don’t need to be an anthropologist to know that these things are relative. Hence, some degree of moral relativity ‘exists’ .Whether it ‘should’ or not is another matter.
I think moral absolutism is a flawed approach. A much better approach is Divine Command theory, favoured by Ockham, Al-Ghazali, etc.- God has given us laws in the OT and NT, and He has authorized the Catholic Church to interpret these.
Moral absolutism denies God freedom to change Laws. For example, if it was morally wrong (i.e. wrong with respect to custom or way of life) for the ancient Hebrews to eat pork, it must be absolutely wrong, and so wrong for us.
But it is not absolutely wrong- it is wrong because it was contrary to God’s Law, at the time. There are no absolutes- God is free to change Divine Law as He pleases.