Just because one is vegetarian doesn't mean they care about GMO, or being healthy, or any of that stuff. This type of classification almost always comes from someone who isn't vegetarian, and its a subtle way of prescribing how they think a vegetarian should think and act.
The rest talk about it about as much as you talk about not eating <something you don't eat for whatever reason> - viz. only if it comes up naturally.
I am vegan and happy to drink Soylent. :-)
Personally, my motivations for not eating meat have precisely zero to do with any "natural" or anti-GMO stance, and everything to do with environmental impact and animal welfare concerns.
Not everyone falls into a nice category.