Rasputin would not really have offered much in way of commentary about the Russian Revolution, as it immediately removed him from his powerful position with Czar Nicholas II. However, one can make a clear case that Rasputin's teachings could offer some insight about the Revolution.
Rasputin achieved fame and a place of importance amongst the Russian royal family because he advocated a spiritual philosophy that suggested that excesses of sin had to be experienced before a sense of redemption could be understood. Sinning had to be experienced before salvation.
Rasputin's philosophy suggests that the Russian Revolution was the form of salvation from the plunging into sin that Czar Nicholas' administration demonstrated. The dissolution of the DUMA, the rejection of the demands of the people, and the failed experience of World War I may have been, for Rasputin, examples of political sin that had to be understood before the intended salvation of the Revolution could be accepted.
On the one hand, Rasputin was an advocate for the rights of peasants and minorities. He wanted the people to have a say in government, such as a constitutional monarchy. He despised the nobility. But he stated himself that he could only work with a monarchy, and had been looking forward to the Tsarevitch being a tsar of the people.
In fact, Rasputin warned the Tsar many times that if he did not make social reforms for the peasants and give the Jews equal rights, rather than slaughtering them, he would have a revolution on his hands.
The "sinning for salvation" philosophy was part of the Khlysty sect. It was not part of Rasputin's philosophy, although he learned what he could of all sects and religions. Labeling Rasputin as a Khlysty was a rumor intended to discredit him, and part of the myth that has been perpetrated about Rasputin. Rasputin was Russian Orthodox, although he felt the church should help all in need, not just the Russian Orthodox.
Rasputin was a healer and humanitarian. He felt he represented the point of view of the common man. Unfortunately, the Tsar was not a humanitarian, despite Rasputin's efforts. Anti-Semitism was official government policy, with laws denying Jews the right to reside where they wished (confining most to the Pale of Settlement), the right to education and many occupations, and often denying them the right to life itself. The military and local officials conducted many pogroms (raids) on Jewish villages, wherein entire families were tortured and slaughtered.
Rasputin thought this ethnic cleansing an abomination. He was also anti-war. In the eyes of the nobility and the bureaucracy, anyone advocating for Jews (who were all considered to be spies), and wanting peace was simply a traitor. The most common method, in those days, of discrediting someone was to conduct a rumor campaign, which the nobles did in spades. Unfortunately, those rumors are what became known as history. As we know, history is written by the powerful, not by the common man.
In conclusion, all the things that were done during the revolution - ending the war with Germany, giving the Jews equal rights, and distributing land among the peasants for them to farm - were all recommendations that Rasputin had made to the Tsar, to avoid revolution. So, while he would have agreed with those actions, he was completely devoted to the monarchy and would have been devastated by its upset.