And therefore should be avoided. This means that veganism isn't sustainable because legumes are bad for you and required to get all the protein you need.
When I ran across this claim it sort of caught me off guard, because I recall legumes regularly topping lists (from respected institutions) as having anti-inflammatory properties. I did a quick sanity check on pubmed, and indeed, articles like this one come up as legumes being anti-inflammatory and even a quick search on the web shows legumes as having anti-inflammatory properties. A more rigorous analysis was conducted and the dietary inflammatory index list "legumes excluding soy" as highly anti-inflammatory. So it's a little weird to see it all of the sudden listed as causing "inflammation" and "leaky gut".
The claims regarding "Leaky Gut" (related to legumes) seem to have originated with Amy Myers as a means to sell supplements on her website with what seems to be little scientific basis. Also, legumes are, in fact, typically recommended for the symptoms attributed to leaky gut, which makes sense since the speculation is that "leaky gut" is really just side effects of gut inflammation - legumes are a great food that help with that.
In short, the objective claim that legumes (in particular non-soy legumes) cause "leaky gut syndrome" is somewhat dubious.
If you're allergic to X, then don't eat X. Go ahead and eat something else. It's not a great argument to throw your hands up and say "Well... I can't eat one particular food X, which means I can't go vegan" ...let alone, "someone selling (scientifically unsupported) supplements off their website said not to eat one particular class of foods, so, therefore, I can't go vegan". Eat something else.