Even with the attainment of tango perfection, this particular anxiety may not go away. Take a moment to recall if you know a talented musician or dancer who is debilitated by the fear of being watched and judged. I know many talented people like this. So the ability or the attainment of tango skills is not the issue with this social anxiety. Skill is indeed needed, but it is to put the feeling of being judged to rest! And it does take skill. Fair and kind self-talk script writing is a great skill. Below, I am going to suggest a few things that will help you or a friend to develop this skill. You can write the new scripts all by yourself, and if that does not work, a life coach or CBT therapist* can help you.
Here's a video that gives the feeling of judgmental eyes very well: