Muslim Revolution
1979
As secular Arab and Muslim states throughout the Middle East displayed corruption, repression and incompetence, more radical forms of Islam began to come to the fore. The Muslim Brotherhood, founded in Egypt, sought to topple the secular regime there and in Syria. This led to further cycles of repression and authoritarian rule within these countries. A similar cycle took place in Iran under Mohammad Reza Shah Pahlavi. A long standing regional ally of the United States, and the West generally, the Shah was deposed by a popular revolution led by the anti-western Ayatollah Khomeini. This ushered in the world’s first contemporary theocracy. Iran’s Mullahs would spend the rest of the 20th Century in efforts to export their revolution to other Shia Muslim communities.
Time: Mid War
Side: USSR
Ops: 4
Removed after event: No
As USSR
Muslim Revolution is one of the main reasons US players tend to avoid the Middle East. This is therefore one of those cards that derives much of its power from the threat rather than its actual effect. And since it is a 4 Ops card, I am often tempted to use it for Ops instead of the event, particularly if Middle East Scoring has come and gone.
In general, there are three reasons I will play this for the event:
First, when the US controls the 3-stability battlegrounds (Iraq and Saudi Arabia). They lose more influence, and also can’t recontrol both in a single turn.
Second, you have enough influence in the country to automatically take it over. For example, if Iran is already at 4/2, then it goes to 0/2 and becomes yours after Muslim Revolution, instead of going from 2/0 to 0/0.
Third, if the US has no access to the affected battlegrounds and therefore can’t get back in before you. If the US has no influence in Tunisia, Sudan, and Israel, then they can’t do anything about losing Libya/Egypt, and you have a lot of time to control them. This is especially pertinent if it is knocking the US out of the region entirely — but be mindful of Sadat Expels Soviets / Camp David Accords!
Of course, make sure that what you’re doing actually affects the scoring of the region. If the region is tied 3-3, or you are being dominated 4-2, then you’re OK with knocking the US out of two battlegrounds, letting them take one back, and then taking the other. But if you are losing the Middle East 5-1, you need to be able to take both battlegrounds before the US does to make it worthwhile. And if you are dominating the Middle East, then re-evaluate whether you really need the benefit from Muslim Revolution. (Of course, Shuttle Diplomacy throws a wrench into all of this math.)
As US
A notorious bugbear for American players, and a commonly-spaced event. But the threat that Muslim Revolution poses is often overrated: provided the three conditions listed above do not apply, it is usually a null event like Socialist Governments. If you are 2/0 on Libya/Egypt, then you lose 4 influence and have 4 Ops to put them back in. Influence in Israel and Tunisia is a great way to do this.
Note that Muslim Revolution—crucially—does not affect Israel or Lebanon, two great places for the US to hide during the Muslim Revolution. This is partially why Lebanon is such an important country to take in the Early War, since it is the only Middle East country completely immune to bad events until the Late War.
Twilight Strategy 
As US: Sometimes Suez Canal comes out early, completely knocking you out of Israel. Then the battle shifts to Egypt and Iran, as Israel is too expensive to bother with. I’ve periodically had games where, by mid-war, ME is dominated 2-1, or sometimes not even that. In that case, Muslim Revolution can be a killer, as it can really knock you backwards in ME. Rather than space it (and after confirming DEFCON is at 2), I will play it for OPs and place my OPs before the event happens. I’ll then place one influence into as many different countries in ME as possible. This reduces the effect of Muslim Revolution, because even though you might temporarily lose control of a BG or two, you at least still have access. Even better, use two OPs in ME and 2 to break control in another region, and now USSR has to decide whether to pounce on your empty ME countries or react to the broken control.
That doesn’t really sound like a winning play (the last option). If I break control as part of an ops war, I want to pour in the maximum to make it hard to re-control the country. Tiny control-breaks are fine if you think your opponent will coup next turn – US AR7, the USSR when Nuclear Subs are active, etc. Then they have to choose between couping (or playing a Scoring Card / Event) or repairing the damage. But in the case of US-played Muslim Revolution, the USSR is going to be pouring in ops anyway. They’ll spend 1 point to undo the control break then put the rest in the newly unoccupied Middle East. It’d have been better to spend a 2 ops spreading influence around the ME earlier as anchors, then pour all the Muslim Revolution ops into repairing the damage immediately if you can’t afford to space it.
I’ve recently seen this card as a total squib and a monster.
Once, when as US I had literally no control in ME (my opponent grinned whilst he played Our Man In Tehran with impunity) the card was a free 4 Ops;
And once when, as US, I had 4-2 control of Iran and 6-3 control of Iraq. In this latter situation, I headlined Missile Envy, and managed to pull Muslim Revs denying my opponent removing my 10 Ops in the Middle East and locking the region down PLUS scoring 4 Ops in the headline phase. Yeah, it was a good Missile Envy.
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Don’t forget about Gulf states. It’s a bit costly (3 OP) for a US and not of much strategic importance, but it is immune to Muslim revolutions and denies the USSR player an extra VP thanks to OPEC. Beside, it’s next to Saudi Arabia and IRAQ if you ever get wiped out of these two countries.
It’s worth mentioning that Muslim Revolution is unplayable as an event after AWACS Sale to Saudis is played.