Let me preface this with a disclaimer: everyone's experience of anxiety is as unique as they are, and as such the ways of dealing with it are as numerous as the stars.
I have found worshipping in silence with other people a great way of helping my social anxiety. It gives us something in common, and a period of time together where nothing is expected - I don't feel obligated to carry a conversation, or act in a neurotypical manner, because all I am doing is sitting and being. After meeting, cups of tea and biscuits go a long way toward breaking the ice. It's much harder to feel uncomfortable with someone when they're smiling at you handing you a cup of tea, or offering something yummy.
The first time I went to a meeting in a different town - Brighton, with the Young Quakers group there - I had a thought pop into my head during the worship, at the beginning, that I was sitting in a room full of friends I just hadn't met yet. Sharing a silence with people is companionable, even if you don't know each other.
The period of time after worship when we sit together and chat is almost as valuable to me as the worship itself. Among Quakers it is not unusual to speak plainly, so it is much easier to take things at face value. A large source of my anxiety is centred around misunderstanding what others are trying to say, which tends to be much simplified in the honesty of the meeting. When a Quaker asks how you are, they are not simply greeting you - they really want to know, and I haven't met one yet without the patience to listen to the real answer.
I have made friends that I value greatly through Quakerism (shout out to the young Quakers at my meeting, you guys are the best), and the social successes I have had help me to boost my confidence a great deal. I cling to bad experiences like a fly to spider's web - I feel like I'm struggling as I constantly am tangled in the memories of when I've gotten things wrong. The good, low pressure experiences I've had with Quakers has given me strength to break free.
Advices and Queries number 27 says "Live adventurously." For me, there is no better manifestation of that than when I find the courage to go somewhere and do something I've never done with people I don't know - for example, a weekend away with the Young Friends General Meeting that I attended recently. I'm proud of myself for managing it, and thankful to the Friends I've met for helping me along the way, because I know that before I became a Quaker such a thing would have been unthinkable for me.