As far as I know, vegetarians are no more prone to dietary deficiencies than the rest of the population, and tend to have lower rates of diet-related illnesses. The people who tend to get deficiencies seem to do so for other reasons that hold whether they're veggie or not, e.g. very limited diet due to poor cooking skills or a reliance on junk food; poverty; a tendency to extreme diets such as fruitarianism, extreme paleo, and certain diets which are out there for weight loss or health. So if you are living on burgers, fries and toast, and you cut out the burgers, then yes, your diet has got worse, but it was pretty bad to begin with. (And the stories of "my sister was vegetarian but she was really unhealthy until we fed her a bit of chicken" always seem to be youngish people whose diets were madly restricted before they went veggie, and who failed to add in replacement foods. I get very fed up with people assuming that a single person who attempted to live solely on beans on toast is representative of all vegans, especially when I eat a far healthier and more varied diet than pretty much anyone I know.) I'm not saying this is you, though!
I also reckon that even if we look at diet history, there will be a bias with this forum. It's a forum where dietary modifications and supplements aren't just popular, they're the norm. This alone will be enough to cause a selection bias with the kind of people who are likely to join this forum and then be active on it.
I think you'd need very sophisticated research to be able to work out how diet, both current and past, interacts with ME. I do agree that it's an interesting point and very much worth looking into. I think we'd struggle to get worthwhile data from a poll on this forum, though maybe there are certain questions which would work better than others, considering that it's a small sample size and biased sample to boot. I put up that poll about gender and sexual orientation, and even something relatively straightforward like that didn't get remotely enough answers to give us even a rough idea of the gender ratio on this forum, let alone for people with ME generally.
If there was proper research on this, I wonder what sort of patterns would show up? Would we perhaps end up in different subgroups? Do the people who can't tolerate grains have other things in common, or the people who do better on meat?