In my view, although some of the Rishonim applied the rationalist approach to Judaism without limitations, we cannot do so. This is for both practical and theoretical reasons.
The practical problem is that
"there is considerable conflict between 21st century academic scholarship and 21st century Orthodox Jewish ideology."
The theoretical problem is that
"I think that there is an irreducible conflict between the very nature of emunah and rationalism."
I agree with both these points, and think they are problems for rationalists who want to believe in Judaism. But R' Slifkin also writes:
I don't see this as reason to entirely discard the rationalist approach. Besides, it's just not possible to do so; you can't make people shut their minds off, and Judaism does not expect people to do so....Nevertheless, I think it should be accepted from the outset that there can be limits to this approach.
This is the part I don't understand. Asking people to accept that there can be limits to where their reason takes them is, indeed, asking people to shut off their minds. I agree that you can't do that. So how does he still wind up with the last sentence of the paragraph, that there still must be limits?
Rationalism and reason don't really have limits; Judaism does. I sympathize with his aim--to keep rationalism and Orthodox Judaism together--but I think he realizes they don't really mesh well, and this piece just comes across as somewhat confused to me. Either you end up "limiting reason"--which he recommends, despite recognizing that this is irrational and likely impossible in the same paragraph--or you end up compromising Jewish belief.