The mere fact of having a belief is some evidence of its truth, robustly so in a well-maintained mind, when within scope of what the mind was actually trained on. Some beliefs don't have clear explicit arguments going for them, and that's not a reason to ignore them as evidence. Such beliefs are only rational evidence though, a personal argument whose truth is hard to communicate without it already being self-evident to others.
I think the old meaning of "bigot" is very close to this. From the 1828 Websters Dictionary:
BIG'OT, noun
1. A person who is obstinately and unreasonably wedded to a particular religious creed, opinion, practice or ritual. The word is sometimes used in an enlarged sense, for a person who is illiberally attached to any opinion, or system of belief; as a bigot to the Mohammedan religion; a bigot to a form of government.
2. A venetian liquid measure containing the fourth part of the amphor, or half the boot.
I can't really think of a word that describes this. Maybe "dogmatic", "fanatic", "blind faith", or "convicted"?
That's not really specific enough. I would describe it as someone being really angry about something, contingent on a certain belief being true, but then when you ask them why they believe that belief, its very weak evidence or something that is the opposite of an open and shut case or something that could vary depending on context and so on and so forth.
Does "reasons" mean "things that led/lead to the belief" or "things brought up when challenged about the belief"?
In the thought causation sense it would seem to be a contradiction in definition. How do you "hold an opinion" in a different intensity than from where in your person it is coming from?
In the second sense it is important to understand that engaging with the stances as standing for something is likely to be pointless.
What is the most specific word for the phenomenon of when someone holds an opinion very strongly on an emotional level but whose reasons for holding that opinion that seem very weak and don't evoke a strong emotional response?