Church is the very best place to be to work through that anxiety. All the churches I've been a part of make deliberate point to welcome all newcomers.
I have two suggestions, you could go to a large church where you can kind of blend in and avoid social interaction on your first couple visits, if that's what you need. Arrive like two minutes late and you won't have any time to chit chat with strangers before the service.
Alternatively, seek out a small church where the atmosphere is more intimate and less anxious. The people there are probably old folks too, which you might find easier and less of a feeling of social pressure.