Broadly speaking, they were “conservative” because they upheld the system of checks, balances and electoral minority rights. Those are features one tends to appreciate with education and adversity. The first for putting them in context. The second because you may see, first hand, a popular and powerful person being restrained from hurting you by the rules.

The fact that Pompey and Cicero were patricians is irrelevant. None of them really had the interest of the masses at heart. Increasing the grain allotment made Caesar no more a man of the people than becoming a tribune had. Augustus did much more in that regard (he personally paid off the public debt!) and he was no man of the people either.