WOW! It's an awesome question to see. Everyone disagree to give the password. This is 100% correct.

BUT!!! Remember! How we need to handle the BOSS?

I won't go against the boss directly. This will ruin the relationships between both parties. I will first understand the reason why they require the passwords exactly for. And if they really need it, there's no issue. Here's how:

Create new account addressing with their company. Share the password. No worries at all.

Normally, working in a company, they provide @companyname.com account. Do you know they can still see your activities, messages if they wish?

Thus, sharing passwords between client and worker is no harmful at all. It's because we're just performing for them. We're just selling our skills for their product. And the password is the key for their door to lock anytime if they wish to keep their product private and keep away from whenever you leave them. It's just one kind of human behavior. Though, most of us dislike!

But aware! Be bold, stay eagled eye if they really feel I'm the boss I'm always right straight forward to you. Then, I suggest you to have gOOgle on your eye for right company. No complaint at all. This is ethically good for you because you love work and you should not hate somebody attached with that work. Just believe in yourself, you'll get lovable people if you keep good faith and more love on your work.

Conclusion: Manner is what every boss wants to see. If your work is good, then the boss will agree with you if give advice or suggestion. More connected people ... job claps!