Am I correct in thinking that "Dutiful men offer sacrifices" -- i.e., this is about sacrifices offered in a cultic sense?
Perhaps it means that dutiful men give of themselves as opposed to being selfish? That they put the well-being of their family ahead of themselves?
I was really stumped there for a moment because I wanted to translate it as "the men sacrifice dutifully" (but the word tiles didn't match). What would the sentence look like with an adverb?
Probably, Virī sacrificant piē. We know that the piī in our sentence, "Virī piī sacrificant." is modifying the virī because they match in case (nominative), number (plural) and in gender (masculine).