I’ve seen this exact debate show up on Mensa message boards and in Mensa publications. Some people insist that it’s bad to put Mensa on their resume or to advertise their membership to friends and family.
But the majority opinion seems to be that it’s a neutral or positive thing to have Mensa on one’s resume. As for me, I’ve put my Mensa membership on my resume and haven’t had any problem with it. My last boss said he specifically focused on that when reading my resume and wanted to have a Mensan on his staff.
If an employer wants to nitpick, then there are lots of ways he could dislike and/or disqualify potential hires: military service, Young Republicans club, gun clubs, feminist groups, liberal affiliations, religious affiliations, atheist affiliations, etc. In a way, Mensa is less controversial than any of those other affiliations and memberships. In essence, a Mensa membership is not much different from a membership in Phi Beta Kappa or the National Honor Society, or a Summa Cum Laude graduation (all of which were also on my resume). They're all pretty exclusive, and thus potentially snobby or elitist.
To put it another way: A good resume should make you stand out from your peers, not blend in. A Mensa membership gets noticed. If it turns off one employer but piques the interest of 5 others, then that's a net win. And if an employer likes your resume but is worried about you being a snobby elitist based on your Mensa membership, then they call you in for a personal interview and ask you about it. Again, it's a net win since that means you've been noticed and moved to the next hiring stage (the personal interview). You just talk fast during the interview and assure your future boss that you have nothing against non-Mensans.