What do you believe is the underlying and defining moral outlook of all "liberals" or all "conservatives" of whatever nation they find themselves in, and whatever time-period?
This is a particularly interesting but difficult question. Since it is not intended to be constrained either geographically or in time, it seems to me that we must first extract ourselves from our contemporary problems; then elements of answers can be found among Greek philosophers, in particular Plato, but also among the many scholars, scientists and researchers who have worked on democracy, whether from the point of view of philosophy, economics or sociology, for example.
Well, it seems clear that “liberal” and “conservative” cannot be “absolutely” differentiated in terms of their respective positions on any specific issue. A position that is considered liberal in one culture may be considered conservative in another; and within any particular society, what was once considered liberal can become accepted in a conservative ethos at a later time (e.g. no conservative in the West today would question women’s right to own property or to vote, but in the 19th century, these were very liberal positions). This suggests that “liberal” and “conservative” are not defined in absolute terms, but rather in relation to each other. So If we “extract ourselves from our contemporary problems” and go back to the ancients, or to other scholars, as Jean-Philippe Terreaux suggests, then we are simply “re-contextualizing” ourselves in another geographical space and another period in history, and there is no reason to believe that “their” perspectives would be any more “objective” than ours. We wouldn’t want to claim, however, that the distinction is arbitrary simply because we cannot pinpoint specific issues that consistently divide the two sides at all times and in all places. The distinction must reside in the overall goals or underlying values that each side is committed to, which do not change, although how they are applied or "realized" may vary according to the conditions and circumstances of the culture/society in question.