My Shia friends are all on mut'ah contracts. It's considered "engagement". It's totally normal and acceptable in that case because our culture doesn't allow an engaged couple to have intercourse. The reason why they do Mut'ah instead of Nikah is because Mut'ah doesn't allow a virgin girl to have intercourse, but they can "explore". Oral sex seems to be the thing with "engaged" (mut'ah) couples, but you can't go all the way. Under Nikah, they can, Islamically, so that's why the parents go for mut'ah.
My sis had a Nikah for her engagement. Culturally she was forbidden to have intercourse, but he knew that she could, Islamically.
She and the guy did it, and caused a HUGE problem between the families (nearly a forced break up, broke the trust between my dad and the guy and so on). lol and they were stupid enough to sneak into a room while we were all in the house, as if no one would notice them get up at night. It's just such a no-no.
The reason why it's controversial is because of what you probably already know, that you can rock up to a hotel with a guy and have a 1 hour contract. In fact in the hotel districts of Baghdad, if you are walking with a guy (regardless if it's your uncle, brother, whatever) you *will* get asked by more than one person if you "need a room". The person that asks is a "sheikh" that you pay to mut'ah marry you. In Iraq, everyone carries an ID card with their marital status, so they would know if you are married, divorced, whatever, and act accordingly.
BTW don't Sunnis do the 4 wives thing? It's completely mainstream with Shias. Even here in Aus, men legally divorce their first wife, but she stays in the house and they Islamically marry the other.
In Iraq, when they marry again, they just abandon the first woman. It's too common. The girl just goes back to her family, it's jut terrible. Also, men wont divorce them, so they can't even marry after him -good luck trying to get a sheikh to recognise your case.. Ugh it's so horrible