Is it appropriate to privately label persons as “pseudo-Catholics” who declare themselves to be Catholics yet do not share belief in Catholic morality?
Not only is it inappropriate to do so, but it is incorrect. A Catholic is a Catholic because of his participation in the sacraments, especially his valid baptism. His status as a Catholic is not dependent on how well he either understands or practices his Catholic faith. When referring to persons who profess the Catholic religion, it is best to simply refer to them as Catholics, without modifying the noun with an adjective that you personally believe describes their adherence to the faith.
That said, it is possible to label ideas as Catholic, non-Catholic, or even as anti-Catholic. A person who is himself Catholic may hold beliefs that cannot be reconciled with the Catholic faith (e.g., pro-abortion, pro-homosexuality, etc.). These beliefs are not “pseudo-Catholic” because they are in no way Catholic. However, the ideas (not the persons) may be labeled “non-Catholic” or “anti-Catholic.”