I wanted to address the general question without getting into your specific examples of which beliefs require accepting irrationality.

G-d is infinite and we are finite. The most basic thing that we can understand about G-d is that He is beyond our understanding. The Rambam writes in several places (Hilchos Teshuva, Moreh Nevochim part 3) that G-d's "knowledge" is not in the same realm as our knowledge, and we cannot comprehend what G-d's knowledge is. Even the fact that G-d

I once heard R' Yaakov Weinberg explain that this is a function of G-d's existence being absolute while the existence of everything else is not (Rambam Yesodei Hatorah 1:1-5 and 1st Ikkar). Thus, this state is inherent in the nature of existence, and not merely something G-d held back from us.

That being the case, there will obviously be some things that we cannot grasp, because they are beyond the faculties of human knowledge to grasp. The infinite is beyond our grasp, and how an infinite Being could create or relate to a finite creation is also beyond our grasp, and there will therefore be parts of existence which are inherently incomprehensible to us.

I wanted to address the general question without getting into your specific examples of which beliefs require accepting irrationality.

G-d is infinite and we are finite. The most basic thing that we can understand about G-d is that He is beyond our understanding. The Rambam writes in several places (Hilchos Teshuva, Moreh Nevochim part 3) that G-d's "knowledge" is not in the same realm as our knowledge, and we cannot comprehend what G-d's knowledge is. Even the fact that G-d is unlimited is not a description of essence, but just an expression of the fact that we cannot assign any definitions (Vilna Gaon's explanation of אין סוף).

I once heard R' Yaakov Weinberg explain that this is a function of G-d's existence being absolute while the existence of everything else is not (Rambam Yesodei Hatorah 1:1-5 and 1st Ikkar). Thus, this state is inherent in the nature of existence, and not merely something G-d held back from us.

That being the case, there will obviously be some things that we cannot grasp, because they are beyond the faculties of human knowledge to grasp, and a person only understands what he can experience (Derech Hashem 1:1:5). The infinite is beyond our grasp, and how an infinite Being could create or relate to a finite creation is also beyond our grasp, and there will therefore be parts of existence which are inherently incomprehensible to us.