You know very well what they meant. The same 'type' of person is more likely to be into 'cleansing' and yoga and other middle class nonsense that others don't have the time or money to think/care about and will freuquently deceive themselves. "I don't eat meat or any of those fake GMO's! Oh look, a non beef burger!" in the same breath.
I'm pretty sure stu_k knew exactly what they meant, and was questioning the "vegetarian types" the OP was referring to.
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.
Way more people are vegetarian than that - it's just that the same people that are loudly cleansing themselves, contorting themselves, et al. are also loudly vegetarian.
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.
No, what you describe are the vocally self-absorbed. That category can, but not necessarily does, include some vegetarians. <insert obligatory link to a Wikipedia page of logical fallacies.>
Most of the vegetarian/vegans I know are more likely to be glad that Oreos are vegan than to fight against GMOs. Anecdotes != data, but I suspect those two demographics overlap less than you're suggesting.
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.
I am strongly in support of GMOs (sans monsanto) and am trying to reduce my meat consumption (ethical & environmental are the largest causes). I'm really interested in the Impossible burger.