To those thinking it's a good idea to screen out your potential applicants: I'm going to give you a real life example of why the courts need to handle this & will hopefully crack down VERY soon.
I got an unsolicited resume from someone who actually has experience at doing what I've been asked to do. Very impressive experience, in fact the best resume I've gotten for the film company that didn't come from an ad posting. Usually, I get things from actors or potential interns.
So as most people do these days, I decide to do an online look-up on the name. I'd spoken to this person & hadn't had a problem thus far; it's just a matter of waiting on what the powers that be want me to do & perhaps an eventual in-person interview.
I find this person's Facebook page. What I find is this person's "pages," the subjects/institutions/etc. you can become a fan of. Based on that, I get a lot of information on where this individual stands on certain social issues.
Now, for me it's irrelevant unless you're some KKK member or religious fundamentalist. Neither stance would serve you well in an entertainment company that has as part of its mission the creation of films that the black community can relate to (I'd feel like asking if you're really sure you want to work w/us).
Legally speaking, I don't think those sorts of things should matter if you are doing your job properly, listening to the boss & not bringing your politics to the office. Much as I can't stand racists, if the person's not making racist jokes at work or a work event, disparaging other people or not doing their job/listening to all supervisors regardless of race, it's still not my job as an employer to tell you how to live.
But what if some employer like Chick-Fil-A found out someone was gay by one of these searches? Are they going to say "no, we won't hire you" despite that person's background or fitness to do the job? Most people would say that's wrong. Or if you see someone's picture & you learn they are a member of a minority group: would you refuse to interview or hire someone based on that while making up BS about the interview or the experience???
The cynic in me says crap like this happens EVERY SINGLE DAY. I have to wonder why you'd want to make it easier for employers to illegally discriminate. Very easy to do so when you're finding these profiles. Seriously, I want someone to file that unlawful discrimination lawsuit & see how a judge rules on this issue. Career advice articles are just telling people to essentially kow tow to this scheme by hiding who they are & it ticks me off; can't we just make things private? That's how I handle things.
Next thing you know, people will be denied jobs based on their spelling skills in a social media forum, their unwillingness to be marshmallows who never have a view on ANYTHING or the number of kids they have. Maybe they are already; if you have one of those stories, I've love to hear about it.
So if you're an employer with a conscience & a sense of fairness, maybe you should leave people's personal Internet identities alone. Stick to LinkedIn if you're THAT curious.