Islam split into two pieces following the death of Mohammed, based on who got to assume control of the Islamic armies - Abu Bakr, his father-in-law, or Ali, his chosen successor. This was while Islam was still in its early expansion, so there are little enclaves of Sunnis and Shi'as all over the map. The Persians were somewhat latecomers and were principally (but not all) Shi'a, but of course many Arabs are as well inasmuch as it began with them. So what you have in Basra is a weird mix where the religion and the ethnicity do NOT map - Arabs vs. Persians (and Chaldeans, and Medes, those biblical peoples remaining as present-day ethnic minorities in Iran) and Sunni vs. Shi'a. If that isn't bad enough there are Christian minorities of both races, some Manichaeans and even a few Zoroastrian dinosaurs, the original Persian religion that seems to be making something of a comeback after all these centuries.
Travis is correct in that I overemphasized the drive of the Basra Arabs for Iranian control, but there are ethnic Persians in the area as well who are in favor of it and have tried it before. The Iranians have ports of their own, of course, but to snitch this from the Iraqis would mean to isolate them from the sea strategically, which is why many in Iran favor it and never mind what the locals think. They did try to take it on several incredibly bloody occasions during the Iran/Iraq war of the 80s.
The "marsh Arabs" of the area aren't exactly Arabic at all, but the remnants of a people so ancient they reportedly date back to Sumeria. Certainly their building customs are the same as many of those of 2500 BC. These have been kicked around by both sides, due to ethnic, not religious, reasons.
Now layer in a group of thugs posing as religious but not really considered so by either sect, who have been charged with keeping order by terror and who have merrily killed anyone of any ethnic or theological description who they even suspect might constitute a threat to Saddam's basically secular police state. These guys are the ones getting backshot by the people they've been oppressing. They don't have a friend in the world and a hope of avoiding retaliation from their various victims. They might as well fight.