When is a Religious Belief Delusional?

[Neo-Scholastic]

- Unquestionable certainty.
- Resistance to scrutiny.
- Contrary to what is demonstrably false.

bold mine. 
Clarification needed here. If it's to be considered a delusion, wouldn't the thinking have to be contrary to what is demonstrably true?

A mundane example would be if someone holds the opinion that it will rain all of next week. He cannot demonstrate that it is true other than referring to a weather report, which based on my experience, tend not to be all that reliable. Similarly, while at work I may be looking forward to having a cold brew from my fridge at home, but I cannot currently demonstrate to others that I do indeed have beer in my fridge. Neither case involves delusion. I truly believe that otherwise reasonable people can believe in any number of wild ideas, like Bigfoot and alien abductions. Neither can be shown to be demonstrably true. It is not out of the realm of possibility that a large undiscovered primate roams the forests of the Pacific Northwest and it is not inconceivable that a race of vastly superior intellect has managed to make their way to our remote corner of the universe.

There is no certainty or guarantee that your beliefs are true and correct...

That seems besides the point. Very few things in life are certain and religious beliefs are no exception. On that we can agree. Merely having strong convictions is not reason to consider them delusional.

Whenever any religion is up for scrutiny and doesn't pass the litmus test, believers go all on the defensive and immediately close their minds to the facts that science has provided, which can't be ignored by those possessing logic and reason.

I cannot speak to your personal experiences with believers. I too have noticed that is true for a small number of people I know. Otherwise most religious people I know are fairly open minded. I think it is very dismissive to simply dismiss them as delusional or dispossessed of logic and reason.

If things are demonstrably true, as has been tested by the Scientific Method, believers still refuse to come around to seeing the logic and reason for the non-existence of a god or gods. 

I know of no clear demonstrations showing that God does not exist. However, there are findings that undermine specific reasons for believing in God or that certain doctrines are contrary to current findings.

So I pose the following question to you: If you can show me why any of the Greek gods are false, then please do. I'll be happy to use your own reasons and explanations as to why the Abrahamic god you follow is also false. 

That is unnecessary. The powers generally attributed them have largely been undermined, such as causing the change of seasons, or that they set constellations to commemorate various heroes, etc. I would say those attributions are demonstrably false. Nevertheless, it is entirely possible that the Greek gods do exist, in some lesser way, but even if they did I would still consider them contingent beings not worthy of the title of God. That said, I would not consider the ancient Greeks delusional for believing in them.