I agree with **Voyager ** on this. Secular science has proven a very fruitful research project when it comes to explaining the natural world; theistic explanations of the naturalistic world represent at best what Lakatos would call a “degenerating research program.” At worse, theism is a complete and total failure when it comes to explaining natural phenomena. So it is more likely that answers about the fine-tuning of the universe will come from science, not theology.
As you seem to acknowledge, there is rational bias and there is irrational bias. As an example of rational bias, contemporary scientists are rationally biased against the notion of luminiferous ether. It has been abandoned as a hypothesis, and for very good reasons. So if someone comes up with an elegant explanation for some phenomenon, but this explanation makes use of the notion of the luminiferous ether, then scientists are prima facie justified in rejecting this explanation, even (I would argue) without knowing the specific details of the proposal. Similarly, since I have what I take are compelling reasons for believing God doesn’t exist, then I have a rational bias against God, and a rational expectation that whatever explanation is eventually forthcoming for the nature of the universe will be a naturalistic explanation, provided by science.