When my wife and I went to Egypt ~20 years ago and would be shopping for anything, we decided to test this exact thing out. We'd pick a trinket common to any vendor, like a souvenir pyramid, or a ceramic bowl. We'd pretend to not know each other, and my wife would ask the price in English, and I would ask for price in Russian. Russian price was typically 1/3 that of English. And that's the starting price, to be bargained down.
After the test, all of our souvenir shopping was conducted in Russian.
All right, then another story from the same trip. We're in Hurghada, a Red Sea resort popular with Russians. We go out shopping at night (it's hot, so lots of shopping at night). My wife is on the roll to get bunches of souvenirs for our nephews and everyone possible, so she's picking up I don't know, bangles, skirts, scarves, whatever. It's late, I am tired, so we skip the "I'll speak Russian" thing, so I just sit down and she's doing all the picking. The shopkeeper, who was sitting there watching some sort of local prayers on TV is very excited to have an American in his shop, and is effusive with "oh I am so glad you are an American, that's such a great country, with such great people, such generous people, not like those Russians, those stingy scummy Russians, who would take the candy out your baby's mouth, steal the last socks from the laundry, no, the Americans are rich and good looking, just like you clearly are so wonderful..." and he's going on and on. My wife is trying to not to laugh and tries to interject - "oh yeah, sure, of course, but my husband, he's Russian, so..." - the guy just doesn't listen and plows right over - "oh those evil Russians, always taking from us, always bargaining down the prices, we have families to feed, they'd take the last crumpled pound note from the ground, they'd won't give me enough for my wares to keep my grandmother fed", etc. etc. Well, my wife shrugs and lets him continue to dig, while I just keep quiet. Eventually she decides what we get, and the bargaining starts, which my cue to come in. Just a couple of minutes into bargaining the shopkeeper turns to my wife with wide eyes and affronted manner "Your husband! He doesn't bargain like American", to which she replies laughing "That's because he's Russian!"
We have a rep for being 'loud' (read, more extroverted than a lot of societies) but I'd challenge the assumption that we're known to be ruder than most countrys. At most we're more likely to be ignorant of local norms due to less international travel.
I don't think base sexism would explain it, unless the shopkeeper hates women so much he doesn't even want their money. Or are women assumed to have more spending money in Egypt?
When my wife and I went to Egypt ~20 years ago and would be shopping for anything, we decided to test this exact thing out. We'd pick a trinket common to any vendor, like a souvenir pyramid, or a ceramic bowl. We'd pretend to not know each other, and my wife would ask the price in English, and I would ask for price in Russian. Russian price was typically 1/3 that of English. And that's the starting price, to be bargained down.
After the test, all of our souvenir shopping was conducted in Russian.