Agnosticism IS the most dishonest position

[Belacqua]

But, if this scrutinizing body or framework is propped up on premises that can’t be demonstrated, in what meaningful way are those revelations that are approved or accepted by that body different from personal revelations that have not been approved or accepted by it?

I think any worldview consists of a web of things we hold to be true, and some of those things can be demonstrated more reliably than others. 

Science rests (or is "propped up by") the metaphysical proposition that what our senses tell us corresponds in some way with a "real" world. I accept that and you accept that, but I don't think it can be proven without just begging the question. Things in science are tentatively confirmed by correlating them to other things that are tentatively confirmed. If they all work together and the planes don't fall out of the sky, then we assume we're getting it right. 

Sometimes, though, a web of things that seem well-demonstrated comes crashing down. The Ptolemaic view of the solar system seemed to be confirmed any time a navigator made it safely to port by using the stars, or an astronomer predicted an eclipse. It all worked together until it didn't. 

A religious framework will use different criteria, by definition. It will include different types of input than science does, including revelations which have previously been accepted. But once it's been up and running for a thousand years or so, and has been vigorously debated, then its internal consistency will be fairly clear about what new input can be accepted. So those of us who aren't committed to the system will remain unpersuaded, but that doesn't mean that any new "revelation" that comes along will be added to the mix. 

So I guess the simple answer would be: revelations accepted by an elaborate system are different from personal whims, because they are in keeping with the other conclusions mutually supported by all the different elements already in the system's web. You and I may think that too many of its tenets remain undemonstrated, but other people (who are just as smart and sincere as I am) find it persuasive.