Another great question!
Let's look at fans that came and visited the Beatles at their homes in the summer of 1967 for example.
George: He was the nicest to the fans. He seemed to like talking to fans on the one to one basis and disliked the large groups. George was also the one Beatle that was most likely to invite fans inside his house and have an orange soda or a marshmallow pie with him. I think this all came from the way he was raised because you see similar behavior with the way his parents treated the fans.
John: John also would chat with fans that came to his house, if he wasn't busy. Only on a few occasions did he invite fans inside (and the one time George and Ringo were also visiting!). He was more likely to sign an autograph and pose for a photo and then ask the fan to leave.
Paul: Paul is complicated. It all depended on Paul's mood. Sometimes he would yell at the fans outside of Cavendish and tell them to go away. Other times he would stand outside and pose for photos and sign autographs and laugh and joke around with them. You never knew with Paul, but most of the stories seem to be very happy. He had fans walk Martha and Eddie (his two dogs) for him. He borrowed a fan's camera when he was going to Greece. I know he invited one fan to come in the gates and hang out in his garden with him.
Ringo: Ringo was the least likely to answer the door if a fan knocked. He would just ignore it. Even in 1967, Ringo disliked giving autographs. When he was out and about in London, he was more likely to stop and sign something and have a photo taken. But when he was home, he didn't like fans to come by. On a rare occasion he would answer the door to a fan, but that was few and far between.