My DD first went when she was 10 months old. She was scared of some characters and they left her alone and interacted with the rest of us. She liked some so of them and they were great with her. We would mention to a character that baby isn't so sure about meeting new people yet and they would proceed with caution instead of being all up in her face. The only time we had any 'trouble' was with Pluto, she was crying and he kept trying to interact with her, he was sweet and got down on her level but I stepped in between them because the more she cried the closer he tried to get.
It really just depends on the character, the baby and heck the winds I don't know lol. One minute she was fine, next minute she was crying, then back to fine when the next one came around.