I agree that that it is not a 'statement of sin.' Your 'crosses to bear' idea is close to what I am saying, however.
That is my point, partly. The sins of the spirit of the deadly sins. But a 'social issue' means that there is a social dysfunction there. I don't think that the movie expresses the idea that this dysfunction is morally trivial ('nothing wrong'

, just that it is not in a category worthy of moralistic contempt.
Which is a viewpoint derived from the moral perspective of Jesus...and which, of course, does not exclude the idea that a behavior is 'wrong,' but that we should not necessarily condemn the person wholesale.
Despite the rah-rah for Chaplin's 'atheism' when THE KID was made, I think that to his credit Chaplin always felt himself attracted to the person and teachings of Jesus and even considered making a film about him.