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Sorry I can't be more useful, I'm not great with office politics. Either way, this would be an extremely unacceptable request in the Netherlands. I can't find out if it's actually illegal here - it is in some USA states.
For completeness, I will make an attempt to provide a more polite answer. "I am sorry, but I do not feel it is appropriate to share any of my passwords. I can promise that my Github activity does not include anything illegal or detrimental to the company.".
But I wouldn't blame anyone for saying "Are you serious, or is this some kind of test? I'm obviously not giving you my password, and I honestly find it offensive that you should even ask."
My Github contains nothing of interest (that isn't public), but on principle, I would quit before revealing my password. Not without a Glassdoor review and possible legal action though.
Most of the case you gave is illegal in The Netherlands under the AVG (GDPR). There are several requirements for keeping a dossier about personnel, and this breaks most of them. You can find a list of these requirements (in Dutch) here: autoriteitpersoonsgegevens.nl/nl/onderwerpen/werk…
I believe this is illegal in many U.S. states, and completely illegal in all countries in the European Economic Area (EEA) under the General Data Protection Regulation (GDPR). If you were to have handed over the password, then your company would have the right to dismiss you, and perhaps take legal action regarding handling of their data. They would also have to contact their partners, and perhaps even their customers, if your employer was to even look at unrelated projects.
I concur: "No"... unequivocally absolutely no.
"No, that's illegal"