My daughter has a 10 second delay in responding to any instructions or to perform any activity. This is more visible when she is with outsiders. She is very reluctant to do anything with others.
Kids with sensory issues often have auditory processing issues. They aren't good at separating out background noise they should ignore from important sounds like someone's voice calling their name. Your daughter could possibly also have a language processing issue where it takes her a little longer to comprehend what someone is saying (think of how when you're tired at night at the end of a party and your host says, "Oh, I can tell you a shortcut to the freeway" and she starts talking and you can't keep up with the words--that's what slow processing is like). A hallmark of sensory issues is inconsistency. In one sensory environment, the issues are worse than in another. With people they know and trust, our kids have an easier time communicating and socializing. The anxiety is lessened and they're available to listen instead of focused on their discomfort.