Paging @TedDavis who can back me up on this definition from a historical point of view.
The historical, consistent, and scientific definition of evolution is just common descent (CD). There is has been a great deal of debate over the last 150 years about the exact mechanism, and there is currently a “strategic ambiguity” in effect about if God could be part of that mechanism. Science makes no claims one way or the other on God’s action here.
Neo-Darwinism, the boogieman of ID, with its focus on positive selection has been largely supplanted by neutral theory. This doesn’t mean that positive selection isn’t important (it is), but it does mean there are a large class of features in biological systems that are better understood as neutral drift than the classic evolutionary story of selection. This includes things like overall genome similarity, pathway redundancy, and the precise details of genome sequences. A great primer on this is here.
One of the great features of neutral theory is that it has a very solid mathematical basis. Using evolution (i.e. common descent) as a starting point, and then invoking neutral theory, we can explain rigorously why mice and rats are 10x more different (about 20%) than humans and chips (about 2%). CD (i.e. evolution) with neutral theory explains this perfectly, with mathematical rigor, and testable predictions too. I’ve asked ID advocates time and time again: what design principle (other than common descent) explains this pattern. No one knows.
One of the more stunning predictions of neutral theory, that has been recently validated. is that differences between different parts of the genome should correlate with differences in the rate of mutation across the genome. Phrased another way: genomic difference should match the rate of change. To be clear, this is a prediction that is experimentally verifiable. And it has been verified for humans and chimpanzees. What design principle (other than CD) explains this strange correlation? No one knows.
I’ll point out (as always) scientists continue to revise the mechanisms of evolution, particularly when considering specific cases. A great example of this is the Third Way, that are clearly arguing against both ID and Dawkins, trying to give a more complete telling of evolutionary mechanism. Positive selection is important, but it is not necessarily the most important mechanism. Alongside point mutation, moreover, there are several other important mechanisms too (like horizontal gene transfer, transposons, epigenetics, duplication, copy number variation, etc.).
Defining evolution correctly as just common descent is really helpful . There is nothing intrinsically atheistic about it. CD is also the most historically and scientifically consistent and correct definition.
To be clear, also, I am not adding to this definition abiogenesis (origin of life) or universal common descent. These things are up for debate in the scientific community, and not part of evolution proper. One group of scientists thinks that life arose multiple times (so they do not believe in universal common descent). Another group of scientists severly doubts any natural mechanism for abiogenesis could ever be found. Regardless, evolution is just common descent of all life to a few (or one) ancestor.
In fact, in the entirely unlikely event that ID could make its scientific case that God intervenes to inspire some mutations, this would only be a minor modification to the over all theory. This would be just introduced as another mechanism of change among many others. The evidence for evolution (CD) would be just as strong, because it is experimentally and mathematically rooted (with gobs of evidence) in neutral theory.
(Just to be clear, I do think God could have been directly involved by first cause, but I am very skeptical science could ever prove it.)
More importantly for ID, if neutral theory is true (and it certainly looks like it is), the likelihood ID can make their scientific case is severely damaged. This is one reason why most ID proponents dispute all the evidence for neutral theory. If it was true, all the ID math we have seen falls apart.
So I hope that is helpful. I think you have been working from a Dawkin’s-defined version of evolution. But, thankfully, it is not accurate.