The question of independent thought has little to do with views of any particular group of persons, there is an objective way of distinguishing between an independently minded individual and one who slavishly conforms to the views of others.
The question of whether this or that particular person is an independent thinker should be answered on the basis of a continuum rather than a dichotomy. Everyone is an independent thinker to a certain degree. You may ask how independently minded must you be in order to be considered an over-man? That question isn't very important, the more of an independent thinker you are, the more of an over-man you are. The over-man should be seen as an inachievable ideal of completely independent thought
, a person should not try to meet this ideal, but to get as close as possible to attaining the cardinal virtues of this Nietzschean hero. Independenc of thought is certainly one of such positive character qualities.