I'm not actually Catholic, only a prospective Catholic, and it's very possible that I'll never get around to actually getting confirmed; it seems like it would be consenting to the categorical rule of propping up institutions even when you're still rather unsure of how good they are compared to how good you should have expected them to be. I grew up agnostic and at some point identified as atheist, only converting to theism and gaining interest in religions besides Theravada Buddhism after I became a postrationalist one or two years ago; I haven't had enough time since then to come to any firm conclusions about the justification or lack thereof for converting to a particular religion.

Put another way: what of Catholic doctrine counts as as "largely some really tricky game theory" and what counts as actually true?

Oh, gosh. Um.

• I think it's plausible that there is a God in the Thomistic or Leibnizian or Kantian(?) sense, and my intuition says there is. I think it's probable that there is an entity, identifiable as YHWH, Who seems to indicate that He is the Holy Ghost (Who is the optimization imposed on the physical world by the existence of that Thomistic God), but I have no idea how much evidence I should accept as enough evidence for His implicit claim to be the Thomistic God. There's that whole "by their fruits ye shall know them" thing but I don't know what counts as satisfactorily delicious fruit. It seems like Satan or any other transhumanly intelligent entity could just as easily provide the same delicious fruits, so this would seem to come down to some tricky reasoning about priors. I'm not yet familiar with the Catholic writings on discernment.
• On the divinity and general metaphysical status of Jesus as Savior, this would seem to be some tricky reasoning about metaphysics on the one hand, and on the other hand, or more accurately on the other side of the same hand, it would seem to be some tricky reasoning about which Schelling focal points to carve out and hold fast to so as not to fall down all kinds of slippery slopes. I notice that if I or someone as generally prudent as me decided to blindly accept that Jesus was their Savior then that would be sheer epistemic laziness without trying to actually understand the social psychology or game theory surrounding why people would go out of their way to emphasize that a certain man had certain properties and that this is important for certain reasons and that doubting this or even doubting something else that would imply doubting this is like trying to "unjustifiably" undermine the allegedly "justified" thing that they're trying to do. This is like taking a very developed Kantian view of things, and honestly it seems really tricky to do right; I'd trust someone like Vladimir_M to do it better than me.
• I agree in a relatively straightforward way with their cautious eschatology about Judgment Day and the Second Coming of Christ, which I see as straightforwardly mapping onto thinking about a technological singularity and taking seriously its moral implications. Whether or not they were right by coincidence is sort of besides the point, as their emphasis is correct either way. (At some point I would like to talk to the Church to see if they're interested in funding FAI research; unfortunately I'm not sure how competent the modern Church is, nor what factions of it would be competent. Traditionally the Dominicans are impressive.)
• When it comes to supernatural stuff I generally accept Catholic doctrine, at least provisionally, e.g. the emphasis on not engaging in witchcraft or negotiating with demons.

Those are what stand out to me as the most obvious possible points of agreement or disagreement with Catholic doctrine as straightforwardly interpreted, but I might've missed some big stuff.