I feel like the hardest part is additives or stabilizers and stuff like that. Like how most wine isn't technically vegan. Or small amounts of gelatin in things. Or cane sugar processed over animal bones. Egg is used in so many things because the proteins have remarkable properties. And so on.

My personal feeling is that worrying about vegan wine is a bridge we can cross when other stuff has been dealt with, but I respect people who have a harder line on that.