How can one develop cringe immunity?

You seem o be having a focus problem more than a cringe problem. That is what you need to work out. It seems focus is becoming more of a problem than ever before, in a big way. Electronic devices have a lot to do with that. It causes people to have their attention directed for them, and quite rapidly most of the time.
Reduce the amount of time you spend online. Also, break it into segments, a few minutes at a time.
Use the time you subtract from being online to do something slow paced. Read a book with paper pages, not on a tablet or computer. You don’t have to read it all at once, unless you want to. Some people have a lot of success with yoga or meditation. Others enjoy an evening walk, or jog.
You need to find out what works best for you. Understand that nothing is going to cure these issues immediately. You need to stick with each one for a while, a month or more, to give them a chance to help. Your doctor or a counselor might help you organa plan.

It is the simplest process imaginable. All that’s required is ceaseless repetition of whatever process responsible for the anxiety. There’s nothing like routine to diminish anxiety. It’s like learning to ride a bike.

Keep a tarantula as a pet.

I do not understand what you mean by “any awkwardness from the past”. Can you tell me what you mean by that?

@Kardamom for instance an awkward interaction with someone where I accidentally said something inappropriate, or made a fool of myself, or was misunderstood, etc.