“Safety” is its most problematic when more a noun than as adverb. Safety, if it is anything, is found in practices-as-undertaken, i.e., “it’s operating safely.” If the behavior in question reflects a “safety culture,” that noun, culture, is performative and not something in addition to or prior to “culturally.”
Safety is no different from democracy or intelligence. They too act adverbially—“behaving democratically in that s/he, e.g., votes in elections, pays taxes and more”—and “thinks intelligently” (whatever that means in practice). To believe safety, democracy and intelligence are otherwise is like thinking you make fish from fish soup.