Speaking as the citizen of a country with a constitution, I have no comment about candidates who rail on their current job but I would be disturbed if employers started disqualifying employees based on critieria prohibited by law in my jurisdiction (Ontario).

For example, what if an HR employee can see from their public facebook page that they appear to be a fan of LGBT organizations and are interested in same sex people?

This exposes the HR person to information that is illegal to gather in an interview and illegal to use as the basis for job discrimination. You can also use marital status or interest in having kids if you prefer... Doing background checks that are not strictly work related is a huge issue. Your example is work related, so I empathize with your desire to know about it. But looking into non-employment behaviour opens up a huge can of worms... For employees and employers.