I have found a compromise that works well for me when I'm asked to login with facebook. I have created an account that exists solely for situations like this. That way I can use whatever site or app I want and its not connected to me.
It might not be connected to your other personas, but there's still someone at facebook who can piece together what apps and sites you use that require facebook logins, and potentially abuse that data.
Chances are it is connected to the other personas and facebook has a more complete than you think profile, heck they don't even need you to be registered to have a profile on you, from being in registered people's addressbook to going to web page featuring a facebook button they can piece together a profile.
If they did tracking based on IPs, they'd get some pretty screwed up results. My university alone has hundreds of FB users behind a dozen IPs or less. Even my home alone has two.
Yeah, but you're probably the only one who's account is connected to both of those and some other places you've been at various times. Or? (I don't really know what I'm talking about.)