such as the claim that if we believe and state we will become rich that the universe will conform to that statement, something I think is referred to as the law of attraction. I have read very strong beliefs in such mechanism and find them without factual basis and utterly irrational.

The question is interesting, why should you find something rational against statements you perceive as irrational, if you don't want to?
How do you come to oppose this kind of irrationality, or think you have to? Where in the world of technological or machine applications do such views disturb? (And if they do, don't they do it for good reasons? Can good reasons also be irrational?)

Those who think that if they pray to God to fill their bank account bulging next month are welcome to do so if they think so - but in honesty, I don't think they literally believe in this but metaphorically.
They still have to pay their taxes, use the same accounting software or forms and use cars, mobile phones etc. I don't see much difference between talking about the law of attraction and trying to get into vibration with the universe or the request to the great Father. People pray all kinds of things.

Nevertheless, I would say that you seem to be interested after all, and if it didn't bother you, you wouldn't care, would you? I think that what perhaps "disturbs" can have a positive connotation, because there is something in one's own existence that likes to try to clarify the disturbing for oneself.