Correct me if I'm wrong, but isn't researching the background of a candidate beyond the contents of their resume - in other words expecting them to have and inspecting their LinkedIn profile - illegal?
Thinking that the job applicant can control the information flow in the entire process by how the applicant fills out a resume or an application form is one of the biggest misconceptions nonlawyers here on Hacker News have about employment law (again, at least in the United States, the jurisdiction I know best). To the best of my knowledge, there has never been, and could never be, a successful lawsuit by a rejected job applicant if an employer checked back references (for example) and found out something about the applicant's previous PUBLIC, WORKPLACE behavior that suggests that the applicant would be a bad fit for the new job.
All that said, a LinkedIn profile specifically is obviously intended for public information, so finding it and reading it seems morally 100% okay in my book, and I do this all the time. I also google applicants to find their Github profiles if they haven't supplied them, and that seems fair to me too.
We've done somewhat the reverse...we had a script that would use the GitHub API to find projects using certain technologies, measure them according to certain metrics (test coverage, LoC, etc) and resolve them to GitHub profiles which were filtered for location and then reviewed manually. The ones that passed we resolved to LI profiles and contacted about our open positions.
It worked well and almost completely eliminated any discrimination along any protected class. Then again, we may have been violating the GitHub ToS, so a lawyer probably would have dinged us on that. Still, it was such an effective recruiting technique that it may be worth it. And reviewing code in GitHub is so much more enjoyable (and informative) than sifting through resumes.
I'm appalled that you are somebody that hires for a living and you don't know the basic legalities of your profession.
It probably hurts candidates at least a little on the average over the long term, even when they have everything you've mentioned.
Why?
But as the other replies have said, it's not illegal today.
Background checks are different to researching a candidate. They are to check that the person doesn't have a hidden criminal record, for example. Researching their private lives crosses the line.
LinkedIn is different, yes, because it's intended as a professional network publicizing your work. But you better be up-front about looking their profiles up, and even then it's troublesome because profiles often include details you would never put on a resume - such as your photo.
I think you should be very careful about researching a candidate for anything beyond normal background/credit checks.