For better or worse, the dentists I have gone to in recent years don't use it any more. I have some old mercury fillings and at least one newer resin one.
Your link is interesting. It seems like the arguments against mercury amalgam being a problem include:
1) organizations like you listed saying don't worry
2) obvious scammers making a living blaming everything on fillings, even nonexistent ones
3) only 5% of people with fillings having elevated mercury in urine, particularly gum chewers
4) "hypersensitivity or allergy" are the "most likely health effects" but there is not clear evidence for or against autoimmune disorders caused by fillings.
It seems to me that it's perfectly conceivable, at the same time, that there is or has been a scam/cult of mercury fillings causing every possible problem, and at the same time, that they do do something to a minority of recipients that is different from acute mercury toxicity that we know about. There could be a combination of more than normal mercury released and more than normal sensitivity.
Something that would be interesting to research, I think, is the microbiome of people with and without different kinds of fillings. There's been some recent claim(s) about the bacteria that cause gingivitis being linked to Alzheimers.