Volunteering might be suitable for some aspies. People who run organizations to help others generally tend to appreciate anyone willing to help and will be the first to look beyond any "weirdness." Helping others is a good way to get out of yourself a little, too. For me, it prompts me to better appreciate my situation. Life doesn't seem so crappy when I help someone worse off than me.
Church can be a good place, too. Depends...
I volunteer for a community emergency response team. I probably give 1-2 hours a month to the group on a regular basis. Every now and then we have training or refresher courses that take a day or so. Our group includes HAM radio operators. Honestly, it doesn't get much weirder but I love these guys. They are fascinating.
I also volunteer for city committees - POLITICS... Right now, I'm a planning commissioner. I really like this involvement because everything has to follow the Brown Act which makes it all straightforward and not so open to interpretation.
I belong to a rockhounder club. Lots of hermit-types - it's the most interesting group I interact with. I've also done a hiking club (got three dates within two months), tall clubs (focused on dating - a little uncomfortable for me), a photography group, master composters and a garden club.
I recently became involved with an event group that hmmm, I'm not sure how to describe them. I don't have the words. Wastelandweekend.com is their website. I do lots of repurposing of discarded junk - it really taps into my creativity. I've met the most fascinating people from all over the world in my dealings with this event and very little of it was uncomfortable. Almost like magic...
I think one would start with their personal interests and research what's out there. I don't focus so much on getting a significant other and stuff has a way of falling into place, or not. Whatever. I just try to enjoy life. With or without a companion, it's mine for such a short time. Why not do everything?
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Life isn't about waiting for the storm to pass; it's about learning to dance in the rain.