If anything, you were probably feeling safer without being connected 24/7 to all the problems in the world. I'm really skeptical you were more afraid of strangers because you couldn't access public records about them.
No, I'm feeling safer because employers are able to look it up and thus make better decisions. It has nothing to do with me looking up random strangers.
Employers don't look up candidates on google, they look up criminal records with the authorities. It has nothing to do with the right to be forgotten. It was possible before, and it will be possible in the future.
I don't know where you live but here employers aren't allowed to look up things other than what is provided by the applicant anyway. Googling the name and using that for hiring decisions is simply illegal. Just ask all the relevant and legally allowed bits in your application process.