Should I stop inviting her?

Your friend may have some anxiety or confidence issues. It sounds like she really wants to fit it and wants people to like her - getting great snacks for the group. Instead of ditching this person, maybe try an activity in which she is the "expert" and let her lead the activity. This could help her build confidence. Also, just show her that you consider her a friend and she will probably begin to feel more confortable and relaxed in time which will result in her particpating more and having fun instead of being so self conscious. Give her a chance. Everyone needs friends and needs to feel like they belong. Maybe you can be the one to show other people how to treat this person - with respect, kindess and appreciation for her uniqueness.