I do think that we need to maintain a polite, professional, clean (in content) Facebook page for every reason under the sun. I am being totally honest when I say I despise trashy photos, nasty catfights, and swearfests on social media pages, and believe they should be avoided at all costs. However, I still think that it's is an invasion of (potential) employee privacy to demand a login to their account like that during an interview. I could see if a current employee was using their Facebook account in a known way that's embarrassing, detrimental, or a threat to a company- then they would have a right to stop such an occurrence and discipline the employee accordingly.
But employers (at least those in the U.S.) are taking advantage of the more desperate position many job seekers are in today, intimidating many people into sharing information that employers simply have no right to view. It has nothing to do with the Facebook page being appropriate or not- this is about principle. Their basic right to privacy being violated is something many people are accepting due to a shortage of well-paying work, and IMHO that privacy is a dangerous right to give up. I see this with younger people I go to college with all the time. They are far too free in giving out their personal information, far too accepting of invasive authority figures, and know far too little about their own rights. I personally would not sign into my Facebook account for a potential employer. It is akin to wanting to view letters my grandmother wrote me, pictures of my children, or a demand to know what income my husband makes. None of the above would be any of their business, since my Facebook page has nothing to do with my skill set, job experience or education level. As if their pages-long applications and absurd paperwork documentation requirements plus drug, criminal, and credit checks done almost universally today wouldn't tell them enough about people! At some point, American workers will have to stop allowing employers to treat them this way. Sorry to take such a strong position in a forum like this, but invasion of privacy when it is totally unwarranted is a real problem, and society should be more concerned about stopping it.