Can you tell me is a gluten-free vegan diet healthy?

Suit yourself: This is a new cult diet. Anecdotally some people who have no evidence of celiac disease find they feel better / have symptoms relieved when they do not eat gluten. The vegan diet is safe if you know how to supplement, and will cost your health and perhaps even your life if you don't. Don't try to dissuade someone who wants to try it, and if you want to try it yourself, check 1st with your Dr.