I don't think it really matters for admissions purposes whether you block your account. If you have anything on your social media accounts that would be unusually damaging in a professional context, then it's probably a good idea to adjust your privacy settings (and/or posting habits) now rather than waiting for it to become a problem in the future, but ordinary Facebook usage is not likely to be an issue. In my admissions committee experience, I've never heard anyone refer to an applicant's Facebook profile and I've never looked at one myself. I've occasionally searched for information about an applicant online, for example to find a research paper that wasn't included in the application or to get more information about an award that was mentioned but not explained. If I run across something else that seems academically substantive (such as a math blog or mathoverflow account) I'll look into it, but I wouldn't bother to look at Facebook since I don't expect it would include anything relevant.
Can my reluctance to give away some (personal) information be perceived negatively?
Under ordinary circumstances, I don't think anyone cares at all. For all the admissions committee knows, you never post to Facebook, and they wouldn't be interested in any case. It would come across as suspicious if it looks like you are actively hiding something scandalous (for example, if there are rumors going around about terribly offensive things you've said on Twitter, and now your account is private), but that's presumably not the case here.