Aspects of functional paradigms are good for safety critical systems, e.g., using pure functions when possible, when it leads to more predictable and testable systems. Recursion and non-strict evaluation, however, are clearly problematic viz. stack consumption, system load, and execution time; ditto for purely functional data structures and associated functions.
[0] I'm hedging here with frequently, but I'm having trouble thinking of safety critical systems that aren't hard real-time off the cuff… perhaps supervised expert systems, say an automated pathology platform, might count?