For instance, what do you think of someone who doesn't have a Twitter feed at all, and whose Facebook you can't access?
I'd ask in the interview "do you enjoy social networking?" and if they said "No", I'd want to explore what aspects of tech startups they do enjoy. If they said "Yes", I'd just accept that they'd locked it down and move on. I've actually done this.
I think too many people are flipping the fuck out about the Facebook aspect.
I would actually prefer github profiles and mailing list contributions. They're much better evidence of ability, mindset and "cultural fit" within a work team, but there are actually very few devs who have anything to show on that front.
I once asked for a github profile, received the username and... it was empty. Not one project. They hadn't even forked anything. I don't think they quite got the point. :-) I interviewed them anyway, they were pretty solid but they had an air of "programming is just a job" compared to other candidates who were more "I absolutely love coding" - it's easier to get the latter group more fired up about building something cool than it is the former, and so they edged him out. Github was a good early flag for that, and I will no doubt use it in future as a barometer of engagement.
However, it is not the sole arbitrator, and not everybody can commit to coding in their downtime because they have other commitments. So fine, show me what you do have.
I do not want to see "private" information. I want to see public information. I am not going to ask to sift through all their holiday photos. I just want to see what they've put out into the public domain, and get a taste of how they think professionally.
The lives of your potential employees are their own, their time spent outside of work belongs to them. That time does not belong to you, it's not on the table, it's not up for discussion. It is, in fact, fucking creepy that you feel like that because you're offering a pittance of a salary you should be able to rummage through the contents of someone's life looking for things 'you don't like'.
You have no respect for the lives of your employees, else you wouldn't expect their social network profiles all lined up and waiting for you to hold judgement over, looking for 'barbaric rituals' and other unfunny comments. It's that simple.