"How are you doing?" and "How is it going?" are correct things to ask when shaking hands (especially with people you have already met, like your fellow church-goers).
Many people treat these questions as perfunctory greetings (like "Hello") instead of as genuine questions. Thus, it is OK for people to not respond to them; they probably do not even realize you asked a question. (I sometimes get strange looks when I treat "How are you doing" as a question worth a short but thoughtful answer.)
"Howdy" is a less formal version of "How are you doing" that has become a synonym of "Hello", and so is rarely treated as a genuine question: