When I was sixteen, I went to Italy on a summer assignment for the JDC, teaching kids Hebrew at summer school. While there, I got to know some of the rabbis of the Habad mission that was based in the town we were running the summer school in. They were very nice men, and they made me pretty welcome despite being more or less a godless heathen (in micro-mini sun dresses, what's more). I thought they were decent enough guys.
Then one day they were all standing talking to a new rabbi that I've not met before. I stopped to say hello to them, and they introduced me to New Rabbi Guy. Instinctively, I profferred my hand for a handshake.
New Rabbi Guy, smiling: "I don't shake hands with women".
Me, embarrassed: "Oh".
New Rabbi Guy: "I only shake hands with my wife. But even that, not always! Ha ha!"
The Other Rabbis: "Ha ha ha ha!"
Me, even more embarassed now for being laughed at: "Wait, why not?"
Rabbis, en masse: look away, change subject.
It took me years to understand why this is, and when it was eventually explained to me, here's how the explanation went:
When a woman in menstruating, she is unclean. She in unclean for several days after menstuating, too. Seven days after she stops bleeding, she needs to go to the Mikvah, to ritually cleanse herself from her uncleanliness.
During the time she is unclean, any man who touches her is contaminated. He would have to go to the Mikvah himself and also be ritually cleansed.
However, women don't show when they are unclean. Sometimes, they don't even know themselves, because e.g. their period has started but they haven't noticed the bleeding yet. So if all men touched all women, they'd be potentially contaminated by their uncleanliness (in Hebrew, they use a stronger word, "tum'a" - it's more like filth or obscenity) and, just to be on the safe side, would be popping in and out of Mikvah like so many hyperactive frogs. To save them the inconvenience, it has been decreed that fathers cannot hug daughters, nieces cannot prop up uncles, cousins cannot kiss on meeting and strangers cannot sit next to each other on the bus (in fact one of the more recent "innovations" of the Jerusalem orthodox community is segregated buses, with women - surprise! - relegated to the back.
The exception for members of a household (not necessarily family) are because it is assumed that those living together will be in the know about the cycles of cleanliness and uncleanliness of members of that household. But there are exceptions even here; one of my ex boyfriends had a sister of became ultra orthodox, and she and her husband never slept together in the same bed, never touched each other, and only had sex once a year (on a date calculated by their mystic-like rabbi), through a sheet with a hole in it. I've seen the sheet.
These guys were pretty nuts, and they eventually decamped as a group out of Jerusalem and moved to a tiny isolated settlement where they more or less lived as a closed cult. So don't get it in your heads that all Jews have sex through a sheet - but some do, and they do it not because there is something wrong with sex, but because there is something wrong with women.
It's one of those dreadful, misogynist, retrograde shards of coral that lurks below the waterline in Judaism, ready to lacerate the foot of the unwary swimmer. Judaism in general has the image of a joyful, communal, positive creed, and there is a lot of truth to that; there is a huge focus on the family, on food, song, dance and merriment, increasingly so the farther you move out into the ultra observant, esoteric, or mystical sects. But even those happy things can sometimes be contaminated by the inheritance (from, yes, Leviticus - bloody idiot that he was) of a deep and abiding fear of and loathing for women and all things feminine.
For example, there is Sheva Brachot. It's a Jewish tradition that I used to find particularly charming. Basically, for seven evenings after a wedding, the friends and family of the bride and groom come together to celebrate their union. There is eating, drinking, singing, saying of blessings and general merrymaking (not to mention intense matchmaking) every night for that whole week, each one traditionally held in the home of a different friend/relative. It's a mitzva and a sgula to hold these parties, as well as to come to them. Sounds great, right?
Well, somebody explained to me why that custom came about. Apparently the blood from the torn hymen makes a woman tme'a - unclean. She remains unclean for seven days, whereupon she goes to the Mikvah and all is well until her next period. Oh by the way, I forgot to mention that the wedding date of Jewish couples is set only after the rabbanit (traditionally the rabbi's wife, but in Israel she can just be a civil servant) talks to the bride to be and gets the date of her periods, so she can make sure the bride will not be unclean on the wedding night - or the groom couldn't preform his marital duty.
So yeah anyway, she's clean, he fucks her, it hurts, she bleeds - and that makes her unclean. The purpose of the seven night long party is not, as you may have perhaps been imagining, to cheer her up, or to keep up the spirits of both bride and groom as they embark on their shared life. It's to distract the groom and get him drunk enough that he is not overcome by the temptation to fuck her again before she's purified.
Growing up in Jerusalem, you have no choice but to learn to get along with religious people. They are by now the demographic majority in the city, and normal life would pretty much be impossible if you decided to avoid or ignore anyone whose spiritual creed you didn't approve of - of any religion. So despite being a confirmed and dedicated atheist, I know a lot about Judaism, about the different traditions and rituals, I can sing along to many songs, and even mumble some of the prayers and blessings. And I've done it, many times, rather than offend people.
But when someone tells me they are shomer negi'a, especially if it's a man, I know that they do not respect, not so much me as a person, but me as a phenomenon; that they at least tacitly agree that my body is the vessel of sin and evil, that my natural being is obscene, that the process that leads to their precious fertility is abhorrent, shameful, dirty and disgusting in their eyes. Forget them not wanting to touch me - I don't want to touch them.