In regards to what is left and what is right (pun not intended but fitting ;)) there is a lot of confusion. And it is confusing, depending on the era of history which you examine, etc.
In general however, when talking about the Church those who favor tradition (Latin (or at least accurate literal translations and not “feel good”), women covering their head, No EMHC, No communion in the hand, altar rails, etc) are conservative, while those who favor novelties (liturgical dances, new translations, laity participation, a loosening of sexual morality, ordination of women) are liberals. Liberal Catholic really is a contradictory of terms in my opinion.
In politics however you need to understand that there are a whole bunch of different liberals and conservatives. In the conservative party for instance there are the neo-cons and the paleo-cons. The neo-cons favor free trade for instance, believing that it helps businesses and ultimately the people as well. While paleo-cons, like those conservatives from the early 20s, believe in helping American business (lowering taxes, less regulation, etc), but keeping them American (meaning tariffs, and no out sourcing). In away they are both trying to help the businesses, and even it could be said the people (trickle down effect) - but, IMO, the paleo’s position is better because it provides a controlled environment for the American Economy, less reliance on foreign manufacturers, and jobs for Americans (again, Neo’s believe per the Honkong example that more white collar jobs are created, but then again…there is more reliance on the rest of the world). The only liberal I really know, however, holds a favorable view on tarriffs as well - but that is understandable, because it reduces “American interests” in other parts of the world. Which would reduce war. I can also assume that he believes that it would give the environmentalist’s more control - but that is just speculation.