Various comments-
1. I think that Luke got the info about the registration wrong. It happened in 7 AD, too late. But it happened at least 50 years before Luke wrote.
2. There was no inn. The word means upper room, the main living quarters of the house. The stable was the cave underneath where Mary could have some privacy.
What did the shepherds think? They were told the Messiah was born – he who would deliver Israel. From who? Herod? The corrupt priests in the temple? What sort of deliverance do we want in our lives?