https://en.wikipedia.org/wiki/Police_power_(United_States_constitutional_law)
"In United States constitutional law, police power is the capacity of the states to regulate behavior and enforce order within their territory for the betterment of the health, safety, morals, and general welfare of their inhabitants. Police power is defined in each jurisdiction by the legislative body, which determines the public purposes that need to be served by legislation. Under the Tenth Amendment to the United States Constitution, the powers not delegated to the Federal Government are reserved to the states or to the people. This implies that the Federal Government does not possess all possible powers, because most of these are reserved to the State governments, and others are reserved to the people."
Last I looked, 40+ states and many metro areas had imposed some sort of stay-at-home order, encompassing 95% of Americans. https://www.businessinsider.com/us-map-stay-at-home-orders-lockdowns-2020-3
Plenty of Republican governors among them, not to mention leaders of countless cities and counties. Looking after public safety doesn't make one a RINO. Or, if it does, then your definition of the word "Republican" is whack and puts you far to the right of even President Trump.
Hope this helps