The big picture, I think, is that common ancestry is evidentially prior to natural selection in Darwin's theory and in contemporary evolutionary biology as well.

Evolutionary theory, properly understood, does not conflict with the idea that God occasionally intervenes in nature - for example, by once or twice causing a beneficial mutation to occur. Biologists have not detected any such interventions despite the data and theory they have assembled about mutation. However, I think it is a mistake to expect biological experiments to be able to detect such one-off acts of divine intervention, especially if those acts occurred in the distant past. Science isn't in that line of work.

Current organisms have a higher probability of sharing a single code if the common ancestry hypothesis is true than they'd have if the hypothesis of separate ancestry were true. That is, the simpler hypothesis has the higher likelihood in the technical sense of "likelihood" used in statistics.

"Tiger is a natural kind" and "Tiger is a historical particular" are incompatible with each other, and evolutionary biology provides a reason for favoring the latter over the former.

Trait X is fitter than trait Y in a population of organisms if those organisms have other biological traits T and live in an environment that has properties E. The theory of natural selection is filled with statements of this form.

Unfortunately, philosophers of science usually regard scientific realism and scientific anti-realism as monistic doctrines. The assumption is that there is one goal of all scientific inference - finding propositions that are true, or finding propositions that are predictively accurate. In fact, there are multiple goals. Sometimes realism is the right interpretation of a scientific problem, while at other times instrumentalism is.

The more evolutionary theory gets called an atheistic theory, the greater the risk that it will lose its place in public school biology courses in the United States. If the theory is thought of in this way, one should not be surprised if a judge at some point decides that teaching evolutionary theory violates the Constitutional principle of neutrality with respect to religion.