If they want your passwords, it would appear that they not only want to see what you have done, but also want to monitor what you may do in the future.
I have read that here in the USA more companies are reviewing everything they can find on the web about a job candidate. If you are using your real name on a web site and have written anything controversial, that can be a problem. It has been a problem for some people whose social sites make them look like party animals.
It is probably OK to ask for a list of your web sites and social networking pages, but to ask for the passwords is going way too far. They have no right to that information. I would not give it to them.
It looks like this issue will die out quickly:
Bozeman city offices have been flooded with angry calls and e-mails since this news broke earlier this week. In an unscientific online poll by a Montana TV station, 98 percent of respondents opposed the city’s request on privacy grounds.
"Democracy is two wolves and a lamb voting on what to have for lunch. Liberty is a well-armed lamb contesting the vote." -- Benjamin Franklin