I disagree. You as a police officer, just like me are free to ask someone for their Facebook password. And that person may tell you or I to go get lost, that they don’t have to tell us.
The fact that you are in uniform and carrying a gun (sees it is GQ) arguably should matter, but it does not. But, if you tell them that you will arrest them if they don’t provide it, then it turns from a voluntary question into an illegal threat to violate their civil rights. If you get their Facebook password from them under those circumstances, it was not a voluntary disclosure, but under a threat, and would likely be excluded from trial and fruits from it.
I respectfully believe that you are mistaken in that you can lie to people about factual situations (we have your DNA all over the place!) but not legal questions (just tell us the truth and I’ll give you immunity).