StackExchange Data Explorer allows login with about a dozen open IDs, but, unlike every other Stack Exchange site (in my understanding), Facebook isn't offered as one of the options.
Is there a reason for this?
Facebook authentication is done via OAuth 2.0, but Data Explorer is currently only set up to handle OpenID authentication. However, most of the heavy lifting is done with the help of DotNetOpenAuth, so adding support for OAuth logins is entirely possible - it just hasn't been done yet.
Since Data Explorer is open source, if someone is really interested in having this functionality they're more than welcome to go add it to the relevant controller. Otherwise, provided there's enough interest in this request, I'll put it on my to-do list and see what I can do about getting it taken care of.