I used to stand in line to order herbal tea and try not to show I was hyperventilating, and when it was time to order, I couldn't get words out right, which was humiliating and got me some really disgusted and suspicious reactions. People absolutely look down on people who show too much social anxiety and may even think you're a creep, especially if you're a guy.
I worked with an older student with dyscalculia who would start pouring in sweat when he tried to count, from all the accumulated shame of schooling and working at a cash register and not knowing how much money he had or who was tricking him. That's social anxiety with an easily identifiable cause. After a few weeks working with me once or twice a week, he was relaxed, better at counting (by 1s and 2s and 5s and 10s) and simple math operations, and didn't drip sweat on the table anymore, or show any sign of that.
Nobody wants to feel socially anxious - or, in vague terms, "insecure."
We should pause before we use "insecure" as an insult. That isn't really fair unless the person is being a big jerk. "Insecure" is not an insult or even abnormal, and I'm not entirely sure that it's appropriate to see it as weakness, either.