I don't think vegan diets are inherently good or bad for hair.
On one hand, there's studies with phytoestrogens promoting increased T and masculinity in males. So I can see a diet high in soy being problematic. But then again, lots of plant foods contain equol which can bind to DHT and help hair.
Vegan diets are generally more alkaline and can reduce inflammation. Question is, is it significant enough to help hair? Again, probably depends.
Low fat diets, particularly very low fat diets might be good for hair (80/10/10, McDougall, Esselstyn, etc). The less fat the less that hormones can be produced. If you have female hormones, this might be bad. But if you're an androgen machine then it probably helps. Then again, you might feel crappy as a male if you reduce your T levels, so there's also that.
All in all I don't think it's going to make much of a difference as this is a means of addressing the issue in a very indirect manner with multiple stages of metabolism to go through before affecting the scalp. Very low fat is probably the safest of these for hair but who wants to have to constantly eat just to maintain energy levels that are lower anyways? I ate that kind of a diet before I even noticed hair loss, but I was also exhausted. But hey if hair is the only thing you care about then it might be worth it.