I could understand if it was Dostoyevsky “keeping it real”. But Tolstoy wrote about and embraced the aristocracy.
Leo Tolstoy's early life and his major literary works are certainly about the aristocracy, but those views changed in his life as he aged and reflected. In Tolstoy's A Confession, his first non-fiction work, mostly reflections on life and death, he quotes Arthur Schopenhauer's beliefs on righteousness. Schopenhauer says "Therefore those who were greatly in earnest about their eternal salvation, chose voluntary poverty when fate had denied this to them and they had been born in wealth. Thus Buddha Sakyamuni was born a prince, but voluntarily took to the mendicant's staff; and Francis of Assisi, the founder of the mendicant orders who, as a youngster at a ball, where the daughters of all the notabilities were sitting together, was asked: "Now Francis, will you not soon make your choice from these beauties?" and who replied: "I have made a far more beautiful choice!" "Whom?" "La povertà (poverty)": whereupon he abandoned every thing shortly afterwards and wandered through the land as a mendicant." This quote in a particularly reflective writing of Tolstoy's is the first hint that he's embracing an ascetic philosophy, at least in idea.
In 1884, Tolstoy published an essay titled "What I Believe" which embraced Christ's Sermon on the Mount, and outlined Tolstoy's personal Christian views of nonviolence and loving your enemies. This essay also criticized the church as an institution and suggesting that they had moved away from the original teachings of Christ. By 1894, he had written The Kingdom of God Is Within You, a philosophical text encouraging society based around the literal interpretation of Christ's teachings, not the church, which includes a rejection of private property and wealth, as hinted at in A Confession.
Tolstoyan movements also started picking up momentum during these writings. Religious communities that followed Tolstoy's teachings sprouted up in Russia and elsewhere in Europe, and were groups that Tolstoy took great pride in (but urged to reject a specific doctrine, and encouraged free thought) and spent increasing amounts of time with in his later years. These groups were also celebrated by other non-violent religious groups like the Quakers and even Gandhi.
In his later years, after this photo was taken, Tolstoy wrote essays such as "I Cannot Be Silent" which rejected the idea of capital punishment and private property. Tolstoy rejected his early major novels Anna Karenina and War and Peace as being artificial, and not indicative of real life. Ultimately, Tolstoy abandoned his wife and wealth, caught pneumonia at a train station, and ultimately died from the illness. Tolstoy had a moral battle with his wealth and fame, and his idea of living a right life, and the best way to do so. I am not certain if this photo is indicative of his style of dress at the time, but I would suggest that it was his way of making his best attempt at living the morally right, ascetic Christian lifestyle that he advocated.
Sources: Christoyannopoulos, Alexandre. "The Contemporary Relevance of Leo Tolstoy's Late Political Thought". (2009). Tolstoy, Leo. A Confession. (1879). Tolstoy, Leo. "What I Believe." (1884). Tolstoy, Leo. The Kingdom of God Is Within You. (1894). Tolstoy, Leo. "I Cannot Be Silent." (1908).