On all significant platforms I know, condition wait works like this:
condition_wait(locked_mutex, condition_to_wait);
Did you have a platform in mind that works differently from this?
Additionally, when you unlock a mutex before signalling the condition, another thread may be scheduled in between that may invalidate the condition that was signalled. This may introduce a race condition.
I signal my condition variables with mutexes locked because it's easier to guarantee correctness that way.
Unless you are writing hard realtime systems where you can make use of the strict scheduling guarantees of SCHED_FIFO, signaling while holding the lock is never necessary nor sufficient for correctness. The waiter must be checking the condition in a loop anyway.
And if you unlock the mutex after signalling the condition, another thread can be still scheduled in between the call to notify() and whatever-notified-thread-which-starts-to-run (and can still invalidate whatever-conditions-it-can-invalidate). There is absolutely no guarantee whatsoever that notified-thread gets to your mutex first (not that it really should matter for correctness in any sane program BTW).
> I signal my condition variables with mutexes locked because it's easier to guarantee correctness that way.
There is no difference in guarantees in practice whether you notify within or after; I'm not even sure that there is any difference in theory (exactly because the thread-which-was-notified is not guaranteed to get mutex first).
Furthermore, it is a good rule of thumb anyway: hold the mutex for the shortest time possible. The corresponding pattern is to hold a mutex, copy the data you need to a local copy, release the mutex and then do the processing on the local copy. Sometimes, the processing can have unknown dependency and so it avoids potential deadlocks caused by some function called during processing trying to take a lock that is held be another thread.
Basically, never hold a lock while calling functions. You never know what might be hidden behind them now and will be hidden in the future.