There is a distinction to be made, I think, between “Catholic liberals” and “liberal Catholics.” I interpret the former in a distinctly political sense and the latter in a decidedly theological sense. A Catholic liberal is one whose political views tend to the left side of the American political spectrum. A liberal Catholic is one whose views of Church teaching fall outside the orbit of what might be called “orthodoxy.” A Catholic liberal might be one who, for instance, favors single-payer universal healthcare, while a liberal Catholic might be one who favors the ordination of women. The extent to which many Catholic liberals are also liberal Catholics is, in my mind, a further manifestation of the blurring of our language, both political and theological, brought about by Roe v. Wade. In the heyday of the Catholic Church in America, most leading lights in the Church were both politically liberal and theologically “conservative,” in the general sense of simple orthodoxy.
I think the same distinctions between “Catholic conservative” and “conservative Catholic,” with the former denoting an adherence to the conservative political agenda and the latter referring to an orthodox adherence to Church teaching. I suppose that these days that would make me both a “conservative Catholic” and a “Catholic liberal,” which is why I simply prefer the term, “Catholic.”