I don't think that capacity or lack thereof was ever really evident in the film. He did come to respect and trust Schultz but there wasn't much explored that said that that would be impossible for Django to do before hand. We can assume that Django would have major trust issues with white males, and wisely so, but I can't say that that is supported by what we saw in the film.
No, we didn't her Django state that he he (now) loved a white man but that scene where he kissed his hand and touched Schultz' body, I think, said it all. Django was a slave, a field slave, the lowliest of the low. His presumed contempt and mistrust for white people, men in particular, needs no explanation or much illustration.
Schultz helps Django free himself from slavery and hone the skils that would help Django stay free himself and save his wife's life. Schultz, who hates the evil that is slavery and therefore slaveowners, proves it by killing one knowing full well he will likely die for what he has done. He essentially died for his ideals.
I don't think there is much reason to wonder about how Django feels about white men at the beginning of the movie and no reason to qestion or doubt his feelings about at least one white man at the end of the movie. Understand, I'm not saying Django's view of white people/men changed by the end of the movie, but he finds out in the end that he does have the capacity to care for a white man. That, to me, represents "some" growth at least.