It seems to me that Francis is having a bit of fun at the laity's expense. It's like he's enjoying playing a practical joke on those who try to kiss his ring. Notice the smile on his face as he pulls back his hand.

I read on another website this morning which reported that Francis allowed the religious (who were in attendance that day) to kiss his ring - it was only the laity with whom he pulled back his hand.

Really? Not to me!
"Official Vatican TV footage shows that Francis stood in a receiving line for around 13 minutes and received (by my count) at least 113 monks, nuns, and parishioners — either individually or in pairs.
No one appeared to offer any instruction on how to greet him. During the first 10 minutes, 14 people shook Francis’s hand without bowing down to kiss his ring.
In this time, 41 people bowed down towards Francis’ hands, either making the symbolic gesture of kissing his ring, or actually kissing the ring itself.
Protocols evolve and changes can be confusing, especially when most people only meet a reigning monarch (or pope) once in their lives. As we have seen in the past few days, old habits die hard, even when the pope is trying to keep the receiving line moving. So while Pope Francis might not be a fan of hand and ring kissing, he is actually following the lead of John Paul II and Benedict XVI.
Before the Second Vatican Council, it was customary in most countries for both priests and laity to kiss a bishop’s ring upon greeting him as a sign of respect and obedience. But times change, and the gesture can also be seen as furthering clericalism and ties to temporal power. Both Pope Francis and Pope Benedict XVI before him have tried to discourage the practice when the pope is receiving visitors, and Francis was resistant to the practice when he was archbishop of Buenos Aires as well."