I would consider these to be the superimposition of modern political ideologies and labels onto 2 main camps of thought within non orthodox views of Catholicism
Previous posters are right in saying that most major issues of faith and morals in Catholicism are not generally subject to Liberal or conservative political interpretation.
Christianity is a Sign of Contradiction in our culture, and rejects many such modern political ideologies - while at the same time championing some of the issues raised by both sides.
I used to consider myself politically Liberal, and a “Liberal Catholic”. I have now realised the error of my ways.
I remain very much aware of the political importance of social Justice issues, but cannot align myself with any of the main political parties in my area in terms of party loyality. All parties do things and support ideas which are anethema to a christian view of social justice.
For example: No UK political party is Pro Life. None give support to defence of family values.
However in the political interaction, while the church has issued a Compendium on Social Justice, this leaves a massive range for personal political opinion on the best ways to acomplish most political goals, and extremes of right and left wing, liberal and conservative, Socialist/communist/capitalist politics are all corrupt and all are very far from perfect. - of course some are worse than others:
Untempered socialism and communism have been decried as evil by the vatican, while capitalism is called to be tempered pulled back from it’s most idealised forms.
“Liberation Theology” is a branch of Catholic Theology which is very important in it’s approach to social justice, however it gets a bad reputation because some theologians and bishops were rebuked for pushing it to far and falling into heresies which had to be denounced by the Vatican. - However the broader school of Liberation Theology must not be treated as a “Bad word”. The compilation of the Compendium of the Social Doctrine of the Church makes it very clear that many of it’s propositions are right, proper and orthodox interpretations of Sacred Tradition and Scripture.
Some “Liberal Catholics” like the leadership of the LCWR, and the leadership of the ACP have been censured by the Magisterium for rejecting the churches teaching on ke issues of Faith and Morals, including some that have been declared infallibly. In doing so they are not “Liberal Catholics” but in truth risk excommunication making them cease to be catholic at all.
“Conservative Catholic” is a label sometimes used by Catholics who wish to distance themselves from the “cafeteria catholic” or “Liberal Catholic” and these people would b better to drop the moniker “Conservative”. they are simply trying to be Catholic. As faithfull as they can be to Our Lord and the Magisterium of His Church.
Others use this term to describe Traditionalist movements such as the FSSP and the Latin Mass Society, as well as the SSPX, “Old Catholics” and other schismatic groups.
Of these some have been heavily censured, with the bishops of the SSPX having incurred automatic latae sententiae excommunication from the Church for specific violations of Cannon Law. Our Holy Father has lifted those excommunications and tried very hard to bring that group back into communion with the rest of the church. (this work remains unfinished).
Other Groups like the FSSP have been actively encouraged, and again our Holy Father has reminded the Bishops that all Catholics have a Right to have access to the Latin Mass in the Novus Ordo (Ordinary form) and in the Pre-Vatican II (extraordinary form), insisting that all bishops make these forms of the mass available to any groups who ask for them.
Those who label themselves “Conservative” yet denounce the documents of the Vatican Councils (especially V.C. II) are anything but conservative. they are in fact rejecting the very foundations of Apolostic Succession and authority of the combined Magisterium that the Church is built on.
(rejection of the effects of the “Spirit of Vatican II” is a totally different matter. That’s a necessary path that we all must follow and find the true meaning of those (and subsequent) documents as written, without rejecting the changes, turning back the clock, or accepting the heresies and abuses that have abounded in the name of the “Spirit of Vatican 2”).
I would believe that “Conservative Catholics” “Liberal Catholics” and any other form os "{insert adjective here} Catholics are all nothing more than
“Cafeteria Catholics” who make a point of treating the Traditions, Teachings, Doctrines, and Dogmas of our Holy Church as some kind of Buffet from which they can pick and choose the bits they like and reject the ones the don’t like.
Ultimately they are all victims of the same malady the heresy that the churches teachings are not a unified whole in a take it or leave it package, subject to the infallible guidance and protection of the Holy Spirit.
Yes there’s room for a wide range of interpretation and opinions on many many matters: but only within the guidelines and boundaries set by our Magisterium.