The only thing I can immediately think of is that you might have some general setting to do with Apps disabled. If you don't have any Apps on your account, then there's a good chance this is the problem, and I think you should be motivated to try temporarily turning on Platform by turning on Apps on the first setting on this page.
On looking on Facebook, I see it has managed to add the Stellar app. But still, when I try to "connect with Facebook" it opens a popup window which immediately goes away, and it reports "Oops! Please verify your Facebook account and try again." Which I have done ("verifying" apparently means "tell Facebook your mobile number") but with no change. Well, maybe I'll contact Stellar about that.
Edit: This post is obsoleted by this post; please see that one instead.
MIRI are currently holding a donation-matching challenge, until Friday 15th August. You can donate and track its progress by going to the Donations page.
Also, to quote the MIRI Facebook page:
Registering for Stellar requires just a username and password, no e-mail or verification required. To get the free Stellar, you have to have Facebook Platform turned on (see the first setting on this page) and allow the Stellar App to temporarily integrate with your account. Send 1000 STR to 'miri' or their address (gHhshpzDcfRsie2qxjjHqrsTRe3JSCaUeN), and you will get back the 1000 STR. Once you receive back the 1000 STR, you can then remove the Stellar app like any other in your Facebook settings.
Edit: The promotion seems to have been reduced. See these two comments.
Edit2: The promotion seems more-or-less gone now; consider the part of this post about Stellar irrelevant.
I did this and it took me maybe three minutes (including time to take notes). The Stellar website is self-explanatory. If you encounter difficulties at any point in the process, or if I've forgotten some part of the process, feel free to comment on this post to that effect.
To track follow-up on threads like this: If you donate because of this thread, please indicate that in this comment (you can do so anonymously there if you prefer), and feel free to state that you have donated as a reply to that comment.
(If you're thinking free cryptocurrency is too good to be true, and wondering what the founders get out of it: My understanding is the reason this works is that early investment in a cryptocurrency bolsters it, so that giving away some for free at the start is actually a smart thing to do at first for the founders. No gimmicks or tricks about it asking for card details or anything dodgy like that.)