Spending more time with his T would have allowed Dostoevsky to break free from religion. Ti would have allowed him to see the world for what it is, irrespectively of whether or not everyone was religious around him.
Secondly, logical thinking would have pruned away many superstitions within his worldview.
I don't know what superstitions he might have held, but on religion: you seem to think that if "God" exists, then someone will have to prove it; if it can't be proved, then we should leave it behind altogether. Right? The thing is, you're missing out on the essence of religion, which is nothing to be scientifically (dis)proved, as reason/thinking cannot fully grasp it. Many people simply start with experiencing "God", and that is all the proof they need.
Let's say you're a convinced atheist, and that somehow, one day you start to experience a presence. A constant underlying presence unlike anything you have ever sensed before, something that calmly seeks your attention, yet remains in the background. Some kind of "force" or "power" that seems to transcend the personal, the wordly, something that seems almost... supernatural. As an atheist you'll of course try to ignore whatever-it-is, reasoning with yourself that now you're obviously going mad. So you dig deeper into the distractions of the material world, and to some extent succeed in forgetting about the presence. For now.
Suppose that years go by and that you keep living your life as usual, and suppose that you are becoming more and more unhappy, as nothing seems to remain any longer that is of any value. The presence comes back and visits you regularly, and you always avoid it, arguing that you are, indeed, going mad. Then imagine something happens, perhaps a close friend dies, something that makes you feel like there is nothing to live for anymore, and you actually consider killing yourself. The only thing that seems to remain is the presence, waiting patiently, and you know that you are going mad but you don't care anymore so you give up yourself and surrender to it, bowing before it, begging it to help you. Your heart breaks as you do this, you give up all fear and resistance, and the following days you feel more sensitive and more alive than ever. People comment that something has changed with you. In time you will probably name this thing, "The presence", "The force" or even "God". And the following years your life changes dramatically, you are not afraid anymore as "God" is always with you, beneath everything else, the one thing that is constant in your life, guiding you, comforting you.
This is the essence of spirituality/religion as I see it - surrendering oneself to something beyond the worldly/the personal. Now, how could MBTI Thinking let you "break free" from this? You have tried to understand it logically, but you can't. You might have talked to your atheist friends about it, hoping they would "enlighten" you. Surely you have tried to argue with yourself that this is some advanced form of self-deception, a psychological construct, but nevertheless you can't get rid of it. Thinking can in this case only work as a resistance to that which it cannot grasp; it can never "see through" it, as it is itself of the personal, while "God" transcends the personal.
Among many other definitions of religion I've heard, one is: "Religion is a language to express things which cannot be expressed." Perhaps not _the_ definition, but an interesting one, and one that fits well with the INFJ type, where Ti serves only as a way of wording the Ni perception (above person doesn't have to be INFJ, though). When Dostoyevsky says "God shall redeem Russia" it is actually his Ti working to put the Ni vision for positive change into culturally specific terms. Had he lived today in the secular west he would have put it otherwise, but religious language wasn't strange at the time, so that is how he expressed himself.