The MUI-ness will only be broken if you use very long waits, such as 20+ seconds, with lots of players and their units that constantly fire the trigger in between that time.
And remember that local variables are usually good for being able to handle 7 instances of that variable being set inside their function.
A computer program or routine is described as reentrant if it can be safely called recursively or from multiple processes. To be reentrant, a function must hold no static data, must not return a pointer to static data, must work only on the data provided to it by the caller, and must not call non-reentrant functions.
local variables have nothing to do with the locals of the other instances of the same function.
Could you make a bit more clear what are those other things, because I am one of those guys?