Disclaimer: Vegan myself and spend some time in eating disorder research.

Currently, there are roughly three veganism "movements" at the same time: Their main motivations are: (1) animal rights, (2) environmental impact, (3) health. Empirically, the first two are on very stable grounds, the last is somewhat more unstable. For example, there is to date not much conclusive research showing health benefits of veganism vs. vegetarianism vs. diet with low (i.e., once a week) meat-intake. While there is increasingly good evidence that the former three diets have benefits over the standard "western diet".

My hypothesis would be that only the third group ("health") is at higher risk for eating disorders. I don't know of research on the topic and this is just my intuition. This group will likely be closely connected to the general "health/beauty/fitness" trends perpetuated by, e.g., instagram, influencers, certain brands, and the like. These trends itself have been shown to affect views and perceptions on body image, etc. So there is a obvious connection to eating disorder development. While this mostly would affect females, there is also a trend and some preliminary evidence for benefits of veganism in body building which, given the connection between body building, body image, muscle dysmorphia, and eating disorders, might again cause a statistical association between veganism and eating disorders in males.

On the other hand, I don't see a good reason to assume that the first two groups who are vegan out of ethical/environmental concerns should be excluded from ED studies. First, they might actually not be at higher risk for ED development. Second, this will, more and more with rising societal awareness of the terrible conditions in animal "production" and the strong positive impact of a plant-based diet on one's carbon foodprint, limit the number of eligible participants, making research harder. Third, again increasingly so with the number of people adopting a vegan lifestyle, this might actually introduce a bias as studies would then be less representative of the general population because a more or less relevant subgroup was excluded. This might be especially relevant for microbiom studies.

So, in conclusions: Maybe an assessment of the motivation for the participant's veganism would be a temporary solution? In the easiest case, a kind of Likert rating for each major motivation to then exclude those who are mostly vegan for health/fitness benefits? Of course, the correct solution would be to first assess whether my hypothesis above is correct to then apply it in participant selection...

We use food depictions quite a bit and usually exclude participants who do not eat the depicted foods. In other words: We typically exclude vegan participants if we present non-vegan food cues (similar to what David Kolar wrote about the approach-avoidance paradigm).

In a currently running online study, we ask participants about their motivation behind a certain diet assuming the same main motivations that Leon D. Lotter described.

I also think it depends on the study topic. When it is about reactions to food, I think it makes sense to use a comparison group which is either not restricted or matched in terms of vegetarians/vegans (mind the difference of the two control groups). I don't see any need to exclude vegans generally when the study addresses other aspects of the eating disorder such as identity or physical activity.