My family is Lebanese, and Lebanon is actually pretty liberal as far as Muslim countries go. You can drink alcohol and eat pork, you don't have to wear a headscarf if you're a woman, you don't have to serve in the military if you're a man, and Christians are tolerated. Syria was that way too before ISIS took over much of the country. However, some people there are quite religious, and some people there frown upon men kissing women outside their family.
I was happy to find out that Lebanon recently legalised homosexuality, which puts it more forward than most Muslim countries. A lot of younger Muslims actually don't have a problem with people being gay, though most older Muslims view homosexuality as taboo. Still, there probably won't be any gay pride parades in Beirut anytime soon, since a backlash from the more conservative population would be bound to happen.
What might surprise Americans is that Arab men can get away with wearing kohl, which is a type of eyeliner. A lot of men still wear it even after decades of Western influence. I actually like wearing kohl myself. In the Western world, eyeliner (and makeup in general) is pretty much a girl thing. Men can also kiss each other on the cheek or hold hands in an Arab country and not be suspected of being gay. I feel like back in Lebanon and other Middle Eastern countries, men can get away with openly showing their friendship a lot more than men here in Australia.
America always struck me as a very reserved country in regards to men. I mean, in lots of countries men can go to beaches or pools in speedos, and in America you can't do that. Other countries also think it's okay for men to show interest in fashion or the arts, but America doesn't really have that.
That being said, Arab society isn't exactly politically correct. Racism against black people is pretty widespread in Lebanon and elsewhere - definitely more so than in the United States and Europe. A lot of our political figures get away with making anti-Semitic remarks. Censorship is also a problem, and anything remotely pro-Israel is banned, and many of the governments equate Jews with Israel even though many Jews don't like Israel (heck, even some of the ones living in Israel don't!). The most ridiculous was probably when they banned The Diary of Anne Frank in Lebanon. Music censorship isn't too bad in Lebanon, although one of Lady Gaga's albums is banned there. I am a Shia Muslim, and among the Lebanese Shia community, a lot of people actually support Hezbollah. I hate Hezbollah and am disgusted that some of my relatives support them.
Most countries in the Middle East still criminalise homosexuality and in Iran and Saudi Arabia it carries the death penalty. (Still, in a lot of countries, the punishments aren't enforced.) In some Middle Eastern countries it's illegal to be an atheist. The sad thing is that liberal Muslims like myself get ignored in favour of conservative Muslims, both in the West and in the Middle East, although it's also true that in many Middle Eastern countries you can't criticise the government.
Keep in mind that these conservative beliefs aren't confined to Muslims. Many Arab Christians and Druzes hold the same conservative beliefs as the Muslims.