If I use the noInterrupt in my getValues() function, then I can read the values perfectly, but my servo won't work anymore.
Is there a way to use pulseIn with another timer than the one used by the interrupts?
You can use the external interrupt to replace the pulseIn() call. Set it to CHANGE mode and store the value of micros() on the first edge, then take the difference between the stored value and the current value of micros() to get the pulse length. This way you don't have to deactivate the interrupts and your servos still work.
Another way is to just deactivate the Timer0 interrupt but then you have to be careful in programming, because you must not use millis(), micros(), delay() and other functions being dependent on them.