My initial summary and commentary on Tolstoy's What is Art? is below, but I wanted to add a few more comments on my own views in relation to Tolstoy's views in this text.
I share much of Tolstoy's religious belief. I believe in the Christ that commanded us to love, bless, and forgive our enemies. The most authentic religious experience of my life occurred when I looked around at some of my fellow human beings, and felt a connection and an understanding--I saw them in a new way (or perhaps, I saw God in them). So I am standing with Tolstoy when he speaks of the "brotherly union of men," of "that feeling of brotherhood and love for one's neighbor," of "the reverence for the dignity of every man and for the life of every animal," and I believe art can foster this. I would diverge with Tolstoy in his insistence that art should or must foster this progress for humankind. Art can be many things and can convey many things--I don't insist that art convey my or anyone else's own religious beliefs and ethics.
I also disagree with Tolstoy's insistence that true art must be universal. I'm extremely doubtful there is any truly universal work of art (perhaps art that deals with death, one of the few universal truths we all must confront), and I certainly encounter great art that moves me that would not move others. And if you are moved by a work of art that does not move me, I would not deny your authentic experience.
Tolstoy also shows an apparent disgust of sexuality and the female body in his book.
I do not share Tolstoy's absolute requirements of art--what I share with him, I would instead identify as possibilities. I recognize the possibility of the moral thrust of art, the possibility of art encouraging unity of people, the possibility of art to connect us, and thus to change how we engage with each other.