I want to get more involved with organising, but fear that due to my autism I will just be a burden. I'm bad in social interactions and get overstimulated quickly.
It's also hard to make connections as well as an autistic person and when I go to socialist meetings I always gravitate towards the people I already know and when they aren't there I feel somewhat left out.
I feel you, I feel/felt the same way. I am somewhat changing in my approach however. I try to stand up for myself and be more assertive in my communication. Try to just get courageous enough to show up, then focus entirely on the subject, try to forget about behavioral aspects. At a certain point you'll meet a topic or you'll have something to say, which will allow you to represent/express yourself and from that point on just be yourself, the social interaction part will come easier since you are now known regarding the way you speak up and how you are as a party man.
The second part is tough, I don't have an answer to be honest, only to try to be a bit more confident in yourself and try to establish at least enough confidence to have a surface level communication and relationship going to operate party tasks and other doings.
I know easier said than done, but nobody said it's going to be easy. Try maybe not to have too high expectations and know your limits, accept those and work with what you have/can offer. This is my view as an autistic person, but your experience may differ, good luck though, rooting for you! Everyone has a place, if they don't allow you to fulfill your role, it's not the place to be.