My guess is that people would be hostile towards MENSA members due to the implied arrogance it implies. Quite simply, people don't like to feel inferior and/or stupid compared to another person; saying you're a member of MENSA just gets the ball rolling, and it's difficult to get people to stop dwelling on the fact. The effect could be described as wounding their pride, in which case they'll do all they can to regain it; unsurprisingly, this manifests as hostility to whomever made them feel inferior in the first place (even if they did so unintentionally). This isn't exclusive to MENSA, but the correlation is already there in the minds of the general public.
That being said... what exactly is the point of joining MENSA?
No offense intended, but I don't really see the point of a high-IQ society; well, beyond inflating your own ego. If you're looking for a mental challenge, there are plenty of routes one could take; some are academic pursuits (obtaining post-graduate degress), others are very prestigious careers. For example, I'm trying to get going in structural engineering (getting my bachelor's degree after my exams are complete); and doing so will involve plenty of challenges over the next few years (including a master's degree, which is more of an expectation than official requirement). Compared to that, MENSA seems somewhat... irrelevant. At most, it seems to be smug & meaningless pride; there are plenty of other venues if you want to challenge yourself or learn new things, and they don't require you to be apart of a high-IQ society to join them. You just go out and start learning them; starting with an academic institution or even the local library is a good place to start.
Perhaps there is a reason why there's outward hostility towards members of MENSA, if their pride indeed rings hollow. Perhaps they could have some actual accomplishments and qualifications to go along with it, but at that point membership to MENSA would seem superflous or incidental. In both cases, it just seems meaningless; assuming I'm not missing or overlooking something.
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And for a good giggle, here's a classic comedy sketch concerning "MENS"A:
Mike from Canmore applies to MENSA[/youtube]