Scorsese treats his subject in a way that glorifies the fanaticism of his characters, both priestly and not, which makes it impossible to like the movie, or them. During the almost entire running time of the film martyrdom is portrayed as a noble thing, a demonstration of integrity when lying and humiliation provide a way out. The priests disagree about whether tramping on an image of Jesus is permissible but they are both intent on continuing preaching, whatever the cost visited upon their flock.
Garfield demonstrates some amount of doubt as the movie progresses and his deity remains silent. This feels more like Scorsese checking a box that everyone would be expecting than a genuine attempt to explore that corner of Garfield's psyche. I am likely wrong about that, I want to think Scorsese is better than that, but the whole thing was very much mishandled. The most egregious moments are when the heavenly powers actually speak to Garfield in audible voices.
I don't know how Scorsese lives his religiosity. I don't even know if he is religious at all. Had I not known he had directed this I would have thought the director had been fascinated by the worst aspects of Catholicism of the Jesuit variety. The last shot of the movie reveals something that demonstrates, if there was any doubt, that Silence is ultimately about faith, faith in the face of adversity and doubt. It believes such faith is a great, worthwhile thing, one that merits a two hour monument. I disagree.
The script only gets intellectually interesting during the discussions in its last third, when Garfield is confronted with the Inquisitor and Liam Neeson. There is no doubt the Japanese authorities are the villains of the story and the history, but the Jesuits are not blameless either, and it is in the allotment of blame and reason that these exchanges shine. The Inquisitor is not a barbarian fundamentalist but a learned man fighting for the sovereignty of his country. Neeson has become enlightened in the cultural realities of Japan that make it hard to preach Catholicism there. His explanation of how Garfield's converts are not real Christians is one of the movie's highlights and the kind of scene I would have loved to see more of. Garfield is deaf to most of their points. A lot of his arguments are right but he speaks out of emotion and faith, not intellectual conviction.
I'm not sure martyrdom is ennobled in the film. Firstly, it's depicted as a pretty awful thing to endure. This is not a quick death, usually. Secondly, there's no indication that anything comes of it. All we know is what happens on earth. Conviction, perhaps, is ennobled, but our "hero" eventually succumbs to apostasy and is depicted as having lived a long and healthy life. The people on the crosses just die, horribly.
They also aren't preaching "whatever the cost," they're preaching despite the cost. There's a conversation about whether or not they are doing more harm than good and they come down on the idea that these are the already converted, but they lack the ability to preach to themselves and perform the sacraments and stuff. The fathers, then, are just helping their temporary flock's souls, not expanding the flock.
I already talked about my admiration for how well I thought Scorsese handled the God visions. I love that it's not clear whether they are hallucinations or real divine presence, and it's wonderful how even such an obvious approach can still maintain ambiguity.
I'm also not sure that "it believes faith is a great, worthwhile thing, one that merits a two hour monument." Firstly, how dare you chop like 40 minutes off of this thing's epic length!?!?! Secondly, despite what I said earlier, the remainder of Garfield's life, while healthy and long, doesn't seem to be a super great time. I think this is another example of the film's wonderful ambiguity. Even that cross at the end might not mean a pat thing like he was right all along or whatever. The cross will also burn, remember. Perhaps faith is a human thing and dies with the person who believes in it.
You talk in the final paragraph I quoted about Garfield speaking out of emotion and faith, not intellectual conviction. Again, I disagree. While I also think this scene holds some of the film's best bits, I think it is precisely because we see Garfield react in such a human way to Neeson's mannered and somewhat logical statements that makes the scene so great. He doesn't have intellectual conviction at this moment, not anymore, and it is his eventual downfall. You're citing the film's greatest accomplishment and calling it a failing. That happens, we see things differently, all of us, but I just wanted to get a fan's POV out there.