This is a bit of a Red Queen's Race: as the "arbitrary" proper noun becomes associated with property X, people start to respond to it as a generic referent to property X. If I want to avoid those responses by this strategy, I end up having to discard one term after another after another, always looking for a term that people don't have a referent for. It's kind of the opposite of clear communication, and gets tedious after a couple of decades.

It's also possible to turn this around. I was a member of an aphasics support group for a while (while recovering from brain damage) and in general this got framed, not as "my environment is insufficiently supportive of aphasics" but "I need more support for dealing with my aphasia than my environment provides." The difference is at best subtle, but it's frequently the difference between people feeling accused of inadequacy and not.

For what it's worth: I've been to a few Mensa gatherings (a coworker of mine was an active member and invited me regularly) and tend to think of Mensa, not as "people more intelligent...", but people who care more about being intelligent. I was a Toastmasters member for several years, I tend to think of Toastmasters as people who care more about speaking well. I've been intermittently active here for a while, and tend to think of the folks here as people who care more about rationality (and in some cases about behaving rationally). If that perception were more ubiquitous it might help... being implicitly accused of not caring enough about positive trait X is less of a challenge than being implicitly accused of lacking X.