Employers should be able to view the public posts their employees make on the Internet. If people do not want their personal information viewed by the general public, they can simply not post it in the first place. People should be cautious with their personal information and not post sensitive information.
If someone is not smart enough to change their settings to private so that others cannot see what they are doing, then yes their employers have every right to look at what they post and put up to see if they are making a good business decision or not. Change the settings.
Yes, people's Google and Facebook posts should be viewable by employers, if the prospective employees or employees leave their settings to public. They should not be able to look into a person's private messages, because this is no different than demanding to read someone's emails. But if a person puts things on the internet for all to see, employers can get a good picture of what each employee is really like.
Facebook accounts are frequently being used as hiring criteria for employers which can be completely unfair. Many of the posts made on the users account are not factual and could be taken unfairly against an applicant. A better method would be if an employer wants access to a google or facebook account of an employee would be to ask the employee to sign for consent.
I do not believe it is right for an employer to seek access to Google and Facebook posts. What kills me about this evolution is the fact that employers take on the attitude that they own the employee or that they can ascertain rather or not a person will be a good employee based on these posts. I don't think that is necessarily true and I don't think it's fair for employers to feel as though they own their employees or can some how control their lives beyond work hours.