From my experience, social anxiety can be a direct result of growing up transgender.
If you've spent the formative years of your life with a "secret" to hide...
If you've grown up listening to common "popular" opinions on gender and gender roles from family, friends and clergy...
If you've hidden away your beliefs and ideas and feelings about your core identity...
If you've censored your own interests and behaviors for the sake of appearing normal to the people closest to you...
If this is the type of socialization you've received... then why wouldn't you have social anxiety.
I'm not saying that this is true for everyone who is transgender. We all have had different experiences and different backgrounds and different levels of support from our families and loved ones. But I think most of us, especially those of us who are older, have spent some time in suppressing, hiding or denying this part of ourselves.
Speaking for myself...
While other children were learning to reach out and form connections with others, I was building barriers and safeguards against others.
While other children were learning confidence from performing well in their assigned gender roles, I felt like a failure, or even worse, a target for not living up to those roles. And when I did succeed in living up to my role, I felt like a hypocrite to myself.
Growing up I never fully socialized as either "Male" or "Female". ...And so much of how we socially interact with each other depends on the traditional dynamic between Male/Male, Female/Male, Female/Female social role relationships that I found that I could only interact successfully in the small margins where gender made no difference.
Overcoming social anxiety is very difficult and I can't say that I've been as successful as I'd like to be. What I believe is that the key to overcoming it is to live authentically and to be willing to share that authenticity with others. It means giving up the self-censoring and trying to act in a way that allows you to like yourself regardless of what others may think.