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No (or at least: not because the code takes too long, there could still be other problems with it of course).

It will just mean that loop_rate.sleep() will return immediately after the "one state [that] runs on 1Hz" has finished, as there is no more time to sleep.

The function Kalman_Filter.filter_control() is a state machine and one state runs on 1Hz, while the rest of the code runs on 8Hz. Will this crash loop_rate.sleep()?

What makes you wonder whether it will crash? Also: what is a crash for you?