Well Beetle, having never been to Qatar myself, I can only say my impressions of that society are based on descriptions relayed to me by pals of mine who spent some time there while serving in the military. There descriptions of a polite and orderly society basically mirror yours.
As you may remember, I spent four weeks in Egypt and two in Israel in the summer of 1992 studying at the American University in Cairo and the Hebrew University in Jerusalem. Both countries had what appeared to be orderly societies, at least on the surface; yet there was an undercurrent of resentment and hostility in both.
The reasons for this resentment are almost too numerous to mention; however, only a few should be necessary to give you the gist of the problem.
Egyptians resent the fact that their country is unfavorably compared to Israel in regards to Israel's apparent success in "making the desert bloom." "Give us as much financial aid as you give the Israelis," they told us, and we can do the same thing.
Also, they don't really care all that much for European tourists who visit their country and exhibit an apparent contempt for their culture. For instance, since the beautiful beaches of Egypt's Mediterranean coast are closed to nudity, some Europeans refuse to acknowledge the fact that the cultural mores of their host country should be respected, and parade around topless or nearly nude at the public hotels and resorts.
At the sound and light show at the Pyramids one night I witnessed a member of the "repressed Muslim society" force a European woman and her two young children out of some seats near the front of the platform on which we were sitting. In all fairness, I'm not certain he was an Egyptian. This jerk must have weighed 350 pounds. His own wife tried to call him down, yelling "Hakeem! Hakeem!" He responded, "No I make scene! You are European! You will move"
There were literally hundreds of empty seats in the same area he and his family could have sat in...but he wanted to prove a point. The woman, by the way, was married to an Egyptian. Thoughts of bouncing my coke bottle off of his pate were nixed by my partner, who said "Hey...it's his country. No good could come of it."
Most Egyptians I studied with, be they student or instructor, were polite and mannerly. Nevertheless, occasionally we were yelled at on the streets. It didn't happen often, but it did happen more than once or twice. Sometimes by men, sometimes by women.
By the way, the most common type of crime one was prone to fall prey to was having one's pocket picked. However, as a non-Muslim foreigner, I can say I wouldn't feel safe walking through the darker streets of Cairo late at night.
As to the Israelis, their streets were orderly, in that they had little of the type of crime so prevalent in U.S. cities. Political violence was another matter. You could see evidence of it everywhere in the country: from the ubiquitous armed guards and soldiers and teachers everywhere, to kibbutzes surrounded by barmed wire and fences and dug in tanks, to bullet-riddled public buildings.
Palestinian hostility was evident in conversations on the street, although the intifada was taking a time-out while we were there.
At that time, there was a fair amount of resentment by the Israelis toward President Bush I, for he was placing pressure on them to enter into negotiations with the PLO. This was the summer that Clinton tossed his hat into the ring to run for President. Bush began the process of leading the two warring factions of Israel and Palestine together; a process which Clinton brought to completion at Helsinki.
Anyway, there was quite a bit of political graffiti visible in Israel's public "facilities" at that time; none of it complimentary and some of it pornographic.