Is it safe to post my CV online (with my physical address included)? Should I be worried about identity theft in doing so?
Considering that public telephone directories with names, addresses, and phone numbers have been around for decades, I don't think there's a significant risk of identity theft here. You could consider using a distinct email for your resume such that if you begin getting too much spam you could manage it separately, but even that's probably not necessary.
Supporting @eykanal, it is not a big issue since data pertaining to many of the social network accounts are not completely private and many do have access to them for various reasons. One option is to put your university/office address on your CV since your name would in general be there on the university website. Also, as a side point at least do not put your photograph on the CV.
I know many professors and graduate students who post full information in their website copy of the CV, including home address & home/cell telephone numbers.
I don't think posting this kind of information is necessary at all for the online CV. I guess most readers/browsers of your online resume are interested in learning about your background, education, honors, grants, projects, experience, positions, and publications, rather than calling you on the phone, or paying you a home visit. Including your email adress is enough I guess.