Every site you go to, and many you don't (because it routes through them) know your IP address. There are two challenges there:
1) Your IP address changes sometimes. So it can be hard for a site to know. But really, if they see a login to account XYZ from IP address 184.108.40.206, they know that XYZ is at 220.127.116.11. If they see it for a month or so, they can be reasonably certain that 18.104.22.168 is that user's IP at home or work or something.
2) The IP address can't be traced to a particular NAME, only to an account. That is, Catholic Online has no idea if IP address 22.214.171.124 belongs to Jeff Stevens or John Smith. They only know it belongs to Kardinal, who CLAIMS to be Jeff Stevens.
3) Your ISP knows every web site you go to, and can sometimes know your account name, but only if you log in without SSL (the lock you see on the web site). 95% of sites, including Facebook and NOT including COL, use SSL to encrypt their logins. So your ISP can know your COL username AND PASSWORD without much difficulty. They CANNOT know your Facebook login name.
The short version is this. If you choose to have a "Read Only" Facebook account like Val does, using something other than her real name, Facebook has no way of knowing whether it's your real name or not. You just sign up with a fake name, "Friend" a bunch of people, join some groups, and never fill in any informaiton about yourself or say anything about yourself. Facebook would know nothing about you except that someone who claims his name is John Smith is logging in from IP address 126.96.36.199.
Your ISP would know you're going to Facebook, but that's all. HOWEVER, if Facebook AND your ISP got together and correlated the data they have...login to Facebook at this time on this date from this IP to this account...then they'd have real information about you. This has not been done to anyone's knowledge. No ISP has ever given up personally identifying information to anyone about what IP they log in from without a subpoena, at least that I'm aware of.
So Bob, I'd feel reasonably safe making a Facebook account just to keep up with goings on on COL if and when it goes down again. If you're concerned, just use a fake name.
Me? I live pretty much in public. You can assemble a remarkable dossier on me if you wanted to by being my FB friend and knowing two places I like to hang out on the Internet, here and one other forum. This does not worry me. I'm not worth stalking for any reason, by government, corporation, or individual.
That's a lot of interesting information, thanks Jeff. Something for me to consider.