Recently a Lakota Sioux and a Navajo debated this with no clear winner, but neither term was felt to be insulting. Use middle-aged as long as you can. Move cautiously to senior or senior citizen, retired or retirement-age. Still has its adherents among women as well as men. Chairperson is cumbersome and a chair is something you sit on.
Jewish person is safe but lackluster.
Hebrew is less erroneous than it is ambiguous, now denoting a language or a people more than an individual or community. Tried and rejected as a gender-neutral substitute for waiter and waitress. Use it and your spell checker will chuckle, as will your server. Going Dutch and welshing on a bet can give offense, as can Chinaman, mick and limey. And watch out who you call a yuppie, WASP or redneck.