Is it permissible for a person afflicted with alopecia, who has completely lost their hair, eyebrows, and eyelashes, not to attend Friday prayer due to the embarrassment and distress they experience?

It is not permissible for you to miss the Friday prayer due to your illness, because it is not contagious and does not make walking to the mosque difficult. To avoid embarrassment, wear a turban and glasses, go to the mosque early and sit in the first row, occupy yourself with the Qur'an, remembrance (dhikr), and supplication (du'a), and linger a little in your prayer spot after the prayer until most people have left.