How would you define the following type of mind?

It is fairly typical to have an atheist asking what use God is, or informing us that no scientific theory requires his existence.

Neither of which is of any relevance to his existence.

I would say Narcissism because it assumes that the laws of logic and reality is subject to what that individual views as personally useful and/or beneficial. However, I would point out that I find this trend of thinking common in BOTH the religious and the irreligious to some extent. All humans have a little narcissism in them.

In order for it to be a fallacy to reject A, you must first provide grounds to demonstrate the existence of A. It is also a fallacy to adopt A merely because you find a belief in A to be useful, or comforting, or in line with your upbringing, etc.

It's called flawed logic.

There are many people and things not useful to MY life in particular but it doesn't mean they don't exist.

Ignosticism means not caring if God exists.

Utilitarianism means not caring about things that doesn't help your life in anyway.

This is not for you because you are too terrified and angry to even consider it, but for anyone else:

"I contend that we are both atheists. I just believe in one fewer god than you do. When you understand why you dismiss all the other possible gods, you will understand why I dismiss yours." -- Stephen Roberts

No doubt. Atheists thinking is hinged on a CBA ( Cost benefit Analysis ) world view.

I agree, it is annoying when people reject atheism on the basis that they don't find it useful.

You tell us,since you have invented it from whole cloth.