There are several things that influence our predilections, down to the genetic level, but anyone can improve their abilities.
A useful point of departure is what we build our self-image around and what makes us feel insecure. Understanding the standards/culture/values we've adopted allows us to start guiding our growth.
Anxiety's accompanied me for several reasons, and when it comes to worrying what others think, these are what helped me:
1) I'm privileged enough to focus solely on personal worries. Finances are stable, environments safe, etc. Compounded stressors reduce only feed off each other. When I finally switched majors, to something I actually cared about, a good chunk of my anxieties settled.
2) I'm determined to always be myself; I love me
When I first watched MLP, I wondered what people were thinking of my pony desktop; but I never changed it because of that. As time went by without any altercations, and my love for the show grew, I became far less likely to worry about it - and if I happen to get self-conscious, it's not nearly as long. It's become normalized.
This could be it's own point, but I'll just say that the expectations you hold for yourself and others is an important one. As you navigate all the social boundaries people throw around, you learn to see them with holding yourself to them. And when you expect better of people, and embrace yourself, there's less hesitation.
3) I have a great support system. My roommates/best friends never treated me differently after learning I'm transgender. And having them with me when I first wore a skirt in public definitely made it easier. I could focus on them over others.
My parents haven't been as embracing, but they're coming around. I became pretty distant from them after how they were "handling it", but started talking openly with them again. During that time though, I felt more aggressive than usual, and had a sharper tongue to cut down my fears; but that's not what I wanted. It brought a sense of control, but at the cost of my own happiness.
I want to be free. Genuinely free from anxiety and unafraid to be me. We live in this world with others, and are bound to buck heads, but that doesn't mean we should sacrifice our civility. We deserve better than that.
Final words: Life doesn't always pan out cleanly, so you gotta grow as you go. And growth isn't usually linear, so don't worry about making mistakes. Just find what's important to you, and treasure it. If your foundation's strong, and you find good friends, then the rest should fall into place.
Hope it helps a bit, and always here if you want to talk more.
All the best