Are credit unions permitted to remain operational during periods when there are government directives to temporarily suspend activities that are not necessary to sustain or protect life, e.g. Governor Whitmer's Executive Order 2020-92 (COVID19)?

There are no such directives in place at this time. Previous Orders have made exceptions for critical infrastructure workers, as described in guidance issued by the Director of the U.S. Cybersecurity and Infrastructure Security Agency. More recently, May 23, 2021, MIOSHA issued updated Emergency Rules entitled "Coronavirus Disease 2019 (Covid-19)" (Emergency Rules) which prescribes responsibilities relative to in-person working conditions and a variety of expectations of employers for promoting a safe working environment.
New: U.S. Cybersecurity and Infrastructure Security Agency (CISA), Financial Services Sector

(Updated August 2021)