I think Facebook birthday reminders are crap. (Yeah, I said it.) They have de-humanized birthdays.
What does saying "Happy Birthday" mean to you? To me, it is a way to acknowledge someone because I care about them. They mean something to me. I have written down their birthday on my calendar, and I want to show them that they are important to me.
In my opinion, responding to an automated reminder has the opposite meaning. It reflects "I saw your birthday is today" or perhaps "Hey all these other people are telling you happy birthday, so I will too."
Is this always the case? I'm sure it isn't, and that some people are quite sincere in their birthday wishes. But it rubs me the wrong way, and I abstain from responding to it.
I will post a birthday wish from time to time for people I'm not going to see in person. But usually it's someone whose birthday is on my calendar, so I feel ethically okay doing so.