I'm afraid that doesn't help. Unless you're just trying to avoid calling it irrational, my initial objection stands.
If you don't believe because of a lack of evidence, I get that. As for God specifically, perceived lack of relevance is a perfectly sound reason not to worship, but I don't see it as a valid reason for disbelief.
BTW, what do you think of naturalistic God-concepts?
Let me put it this way.
The primary function of spiritual belief is "How should we live". Most people, I think I can fairly assume, have developed various spiritual beliefs to help them determine how to live. I do not have any spiritual beliefs that tell me that. Of course, there could be a semantical argument over what qualifies as spiritual. I equate religion and spiritual. Just for the sake of argument.
In my daily life there is no question, no problem...nothing I do that requires belief in the spiritual realm or the supernatural. In other words, the concepts are irrelevant to my personal life. The quibble may come in that the particular manner in which I live my life can indeed be considered spiritual. Or that spiritual matters are not irrelevant to me since I'm posting on RF.
But those are usually issues of semantics.
The issue over the existence of God is irrelevant to me on how I live my life. I'm not stating that this equates to an irrational mind held by believers. Despite my often glib statements.
edit: The issue over physical evidence is tricky. SuperUniverse already stated that the existence of the universe itself is evidence. There is nothing to debate there.