At no point do I wish to be in conflict with any man or masculine thought. It doesn't enter my consciousness. Art is anonymous. It's not competitive with men. It's a complementary contribution.

This quote means that the speaker does not want to be in disagreement with any men or the things that are traditionally associated with men. The speaker does not even want to think about having conflict with men. The speaker believes that art is not about competing with men or trying to prove something to them. Instead, it is about making a positive contribution to the world.