i don't find it offensive.
A highly offensive smilie. Change it at once. <g>
Seriously, going back to GlasgowBee, I think that there are occasions when 'nuts' is offensive, as was the case in 2002 when there was a fire in a 'mental hospital' and a US paper ran the headline Roasted Nuts (genuinely), or in the ongoing cases NAMI raises against the NY Times and its offensive crossword clues.
I am aware of the book you refer to; against that, I think there are two other points to be made.
First, the mental health industry itself frequently uses the phrase itself tongue in cheek - for example, there is an information site 'Mixed Nuts'. I know that, for example, sectors of society use terms to describe themselves that they would take offence to were they used by 'outsiders'; I might refer to myself as a Jock but would be cross if someone else I didn't know used the phrase about me; but the prevalence of these sort of sites suggest that although some may be offended, the majority wouldn't be.
Second, the phrase 'nuts' has. according to all the dictionaries I've been able to consult, two distinct meanings; 'crazy' (sic), and 'highly enthusiastic'; nor do any of them have the usual disclaimer that this word is potentially offensive. I can't see that a visitor to the site would genuinely believe that 'nuts' on the GPG was meant to imply that many of the people on the site were genuinely ones who had mental health issues.
It's a tricky one, I agree, in part because although a number of my family members have suffered from mental issues, I haven't, so I'm not speaking from a subjective point of view.
However, don't worry about being on a high horse; it's a valid point to 'stirrup'.