Your sentiment is spot on, but your terminology is not. Religion is irrational, which does not mean that it is wrong or that it is somehow overly emotional. It simply means that it does not have a rational basis, i.e. no science or math, but rather a circular argument. Again, this does not make it wrong, it simply precludes a rational basis.
I totally understand the hesitation to refer to a religion as "irrational" because of the popular/common connotation that comes with that word, but in this case, "irrational" simply refers to the underlying basis, saying that it is not science (or math). You cannot demonstrate your underlying circular argument. Of course, you don't have to, but no one's religion has an underlying rational basis.
Yes, but there is a huge difference between someone engaged in a fallacy (which is not what I am claiming) and someone simply without a rational basis for his belief (which is the case when it comes to religion). Your religion, for example, simply is what it is, and it is not falsifiable, ergo it is not rational.
These religions are like Christianity in that they are not rational, but unlike Christianity, they are riddled with fallacies.