Actually, I started thinking some more about symmetric mutual exclusion, and I realize that I was actually mistaken. You don't actually need to use any randomization. Although in a real system, the only way to generate unique thread ids would be to use randomization, JavaScript does have one operation that is guaranteed to generate unique keys--just use new to create a new Object since new is atomic. You can then use this object as your thread id. And since it's an object, JavaScript will automatically take care of cleaning it away once you're finished with it.
So, in conclusion, JavaScript mutexes are possible if you use a shared memory symmetric mutual exclusion algorithm and if you are able to put a bound on the number of threads that may attempt to enter a mutex at any one time. This is the best approach to the problem. There are no unacceptable trade-offs that need to be taken into account (beyond the whole messiness of needing to implement your own mutexes in JavaScript in the first place).
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