A religious response is any reaction to a statement that (superficially at least) entails an ethics of some kind. The ethics might be a social morality (people should wear more clothes and drink less alcohol, the west is an evil colonizer, etc) — or more mystical in nature (it is better to detach from the ego, we should be, not think, etc). Always a “better”/”worse” schema is implicated.
The seal of the religious response — its perfection and apotheosis — is within the Islamic religion, including its offshoots (the Sufi tradition).
Taking this as a very broad definition, it’s quite difficult to avoid a religious response, in agreement or disagreement with a statement. The piece you read before you right now might well be a religious response itself!
There are other responses that go deeper than the religious but are exhibited by religious people: the physical, for example. A physical reaction is one of attraction or rejection based entirely on DNA, pheromones, blood — a reaction to the body that has uttered the statement, rather than the statement itself.
The physical response is about physical compatibility and is biological yet with cultural-spritual implications: can a limb be successfully transplanted from one body to another, will the couple make beautiful children (eugenics), is the speaker of an alien race to threaten the racial purity of the indigenous tradition, etc.
The physical response is responsible for love, as well as hatred. It underlies religion: it is its lifeblood, its foundation. The religious response is, in fact, a byproduct of the physical.