Initial sentence should read, "The influence of social realism in some left-wing groups has imposed some ...." Using the verb has instead of have, since the noun "influence" is singular.

Here's a slightly revised version below. All I did was take out some adjectives (to make the first statement stronger without altering meaning) and slimmed down the second part. Let me know what you think. I understand the point you're trying to make, and honestly it's not a bad start relative to other papers that I've read while in university. The influence of social realism in some left-wing groups have imposed artistic prescriptions and excluded artistic manifestations outside of a traditional and stereotypical notion of “committed art” (Collazos, et al, 1970). Even in the most liberal areas of the society, the process of professionalization has implied that the works of non-university educated artists are not connected to the system of education or the international art scene, thus dismissing the validity of their opinions about art, politics and the city (Baez, 2017).

my phd proposal :)