Okay, but that could mean anything. What isn't a religious issue in a Muslim country? For example, where would honor killings fall?
The difference is in who is bound to obey the faqih when he makes a ruling: just members of the Muslim community who treat that faqih's rulings as authoritative, or everyone in the country, Muslim or not, accepting of the faqih's authority or not.
Iran, of course, is of the latter type. If you're in Iran, and the Guardian Council rules on something, you gotta obey. And if you don't, the Iranian government will make sure you do, via official Iranian governmental organizations like the police and courts.
In secular (like the US) or religious but non-Muslim countries (like Israel), if a faqih makes a ruling, the only enforcement is voluntary within the community. The faqih of a Muslim community here in the States can't call up the cops in Poughkeepsie to, for instance, have a woman arrested for not wearing the hijab, no matter what his religious rulings may say. Where religious rulings and secular laws conflict, the community has to make accommodations to account for what the secular laws say about doing/not doing a particular thing (because they apply to Muslims and non-Muslims alike, whether any of them like it or not).
The aforementioned Ayatollah al-Sistani, in addition to being a leading religious voice in the Iraqi shia community, has a following among shia worldwide. As linked above, he even has his own website, and has often issued fatwa for members of his community who live in non-Muslim countries and often contend with some very modern Western issues in their lives there, and the issue of obeying religious laws vs. obeying secular laws is a very real one for them.
For example, al-Sistani, unlike his Wahhabist Sunni counterparts in Saudi Arabia, thinks it's perfectly okay for women to drive. However, he also thinks that women should not spend time alone with men in public, and should wear hijab, the head covering that leaves faces visible, in public (al-Sistani, while possessing some views that could be called "moderate" on some issues, is definitely not even
close to being a "moderate Muslim" in the sense that Rauf is).
However, in the US, in order to get a driver's license, you have to learn to drive and take a driving test. Driving instructors are usually male, the test is very often given by a male tester, and you can't wear anything that covers your face and head in the driver's license photo (there have been court cases about this here). To resolve that conflict, al-Sistani issued the following rulings:
Q110: Is she allowed to have a picture of herself taken without the hijab to place on a passport, for example?
A: If she is forced to place the uncovered picture on her passport or other official documents, then it is permissible. But, the one who takes her picture must be her husband or her mahram [basically, one's relatives of the opposite sex]. However, should the need arise, it is permissible for her to have the picture taken by a non-mahram photographer
Q118:Is it permissible for a woman to learn to drive a car with a non-mahram man, which necessitates being alone with him and going with him to places appropriate for practice, when these places are normally free from traffic?
A: This is permissible for her provided that she is safe from falling into a forbidden activity.
Of course, this cuts both ways. Al-Sistani believes, as most fundamentalist Muslims do, that a divorce only happens when the man divorces the woman. If he does not want to divorce her (or can't be bribed to divorce her - and believe it or not, those are special named subtypes of Islamic divorce), they're still married, whether she likes it or not. However, in the US, any woman, even a Muslim woman, can phone up a divorce lawyer and get an American court to declare that she and her husband are divorced. So what if our hypothetical Muslim wife does that over the objections and refusals of her husband for a divorce?
Q93: Civil divorce between a man and a woman is finalized according to Western laws, but the man refuses to grant shar'i divorce or provide maintenance to his wife, and refuses to accept shar'i mediation. What is the position of the wife knowing that her patience in this situation is absolutely a cause of hardship?
A: Her case should be taken to al-hakim al-shar'i [ie, the judge of a sharia court] or his representative who would advise the husband to abide by one of the two options -- either he provide maintenance or implement the shar'i divorce -- even if it is through a representative other than himself. If he refuses both options and it is not possible to provide maintenance for her from his property, then the hakim or his representative can divorce her.
In other words, the Western divorce is considered binding as a true dissolution of the marriage, even over the objections of the husband.
Regarding honor killing specifically, I can't find where al-Sistani has said anything one way or the other, though his predecessor in the position of Grand Ayatollah of Najaf, al-Khoei, did rule that the penalty for adultery was death. The big list of subjects that al-Sistani's religious rulings cover is virtually identical to that of al-Khoei's, and while some decisions are the same, others are different. That makes the complete absence of adultery rulings rather curious, but I can't say whether it implies al-Sistani agrees or disagrees, since with only a few other exceptions, on every other topic he gives his own ruling even if it's the same as al-Khoei's.
However, as revealed above, al-Sistani doesn't think that religious rulings should become government rulings, so even if he did support honor killings as a religious decision, someone who committed an honor murder, per al-Sistani himself, would still be subject to prosecution and punishment under the secular law.
I personally find that rather unacceptable, so I hope either al-Sistani doesn't support honor killings, or says something like "well, the penalty should technically be death, but if that's illegal where you live, don't do it" (which is still pretty vile, though at least it's a
little bit less likely to result in actual murders).