Much depends on the sense in which we take the term 'science'. Does it mean 'rationally-held knowledge of any sort', or does it mean 'knowledge derived from physics, chemistry, geology, biology and other material things'. You seem to be arguing for the science-in-the-first-sense here, which I'm basically in agreement with (I may quibble here and there). All knowledge, including the content of Divine Revelation, is rationally held to if it is true knowledge. The goal, the purpose of the intellect is the attainment of truth; thus all true knowledge is rational, while all false knowledge is irrational, and is a failure of the intellect to achieve its end.

But quite a few atheists say that claims about anything that is outside science-in-the-second-sense's domain is irrational. Example: Alex Rosenberg states that any knowledge outside of physics' domain is irrational (in line with his reductionist philosophy, he holds chemistry, biology, etc to be physics on a bigger scale). Hume also seemed to be pushing such views with his fork. This claim is trivially easy to refute, I assume you know the arguments already so I won't waste your time with them.