Orthodox Catholics can’t be compartmentalized as “conservative” nor “republican.” But to your comment, the issues you mention are not cut and dry moral issues as are things like abortion or the definition of marriage, for example.
Thus, “income inequality” isn’t even something the Church considers solvable or necessarily bad. In some cases instances, the inequality may be due to an injustice, but as a broad concept, no. For example:
It must be first of all recognized that the condition of things inherent in human affairs must be borne with, for it is impossible to reduce civil society to one dead level. Socialists may in that intent do their utmost, but all striving against nature is in vain. There naturally exist among mankind manifold differences of the most important kind; people differ in capacity, skill, health, strength; and
unequal fortune is a necessary result of unequal condition.** Such unequality is far from being disadvantageous either to individuals or to the community.**
Social and public life can only be maintained by means of various kinds of capacity for business and the playing of many parts; and each man, as a rule, chooses the part which suits his own peculiar domestic condition. (Pope Leo XIII,
Rerum Novarum, 1891, #17)So, since Pope Francis is a servant of the Church according to his own words, and that his social doctrine merely reflects the Church’s preceding teaching, he would have to give due respect to his predecessor on the same topic. In other words, the concept of “income inequality” is not automatically and objectively evil as would be, say, abortion. The factors of that inequality would need examination to identify if an injustice is occurring.
Climate change is similarly not a clear-cut issue of morality. It is first of all debatable as to the degree of human effect of the climate change. And if so, it is debatable as to what is the best solution, if the human influence is even “bad.” Once again, mere change in temperature is not an objective evil.
If one does not grasp the difference between objective moral issues like abortion versus nebulous social concepts, then one does not understand Church teaching at the outset.