There are two propositions you can entertain here.
1. All cultures are equal in the sense that they are equally as good.
2. There is no way to compare the merits of any two cultures.
(1) is a claim that attributes equal merit to each culture. It is then necessary to establish what exactly these merits are.
(2) is a claim that does not per se exclude the possibility of there being a matter of fact about which culture is superior in which ways w.r.t. other cultures. It denies the possibility of establishing what the fact of the matter is.
(1) admits only two possible presuppositions. Either (a) all cultures are equal because the good they impart onto individuals and societies is ultimately the same and thus differences are merely cosmetic, or (b) cultures are not a good (that is, neutral or inert w.r.t. the good).
(2) admits two possibilities as well. Either (a) our ability to know is limited or impaired or (b) we cannot know because there is nothing to know, i.e., (1b).
I think focusing on (1) in this context is a waste of time because clearly no one in this context actually believes it. Protests have a motive and motives only make sense w.r.t. to some end. As you point out, what's the impetus when change produces no change in the good? Protesters and revolutionaries may hold incoherent and confused beliefs, they may have ulterior motives, they may be wrong, but ultimately there is a belief that what is now is evil and what they aim at is better.
Ultimately, to be able to judge the merits of any culture requires (at least) a sound philosophical anthropology. You need to understand the nature of man to know what he requires to flourish. Only then can you judge whether, in what ways and to what degree a culture enables that flourishing.