It undermines God's authority in the sense that evolution is not a guided process (as it is taught in secular culture). However, the Bible states that God created, not that He caused to evolve. The "science" that supports evolutionary hypotheses is not actually scientifically sound.
"As taught in secular culture"
I agree with your point there.
The "science" that supports evolutionary hypotheses is not actually scientifically sound.
The concept of macroevolution is speculative and inductive like string theory. It takes the concept of observable adaptation and speciation and projects it backwards in time. The models of evolutionary theory certainly don't have the same kind of clout as chemistry, etc. And they stand as something different than most R&D type science.
It is completely reasonable to be uncompelled by models of evolution, but so long as the theory remains consistent with the empirical observations and scripture, it establishes itself as a valid theory. If a model stated "everything appeared out of nothing and God had nothing to do with it" that would be an example of an invalid theory. And I think you're right when you say that this might be the dominant secular model that gets idolized. When we peel away the atheistic concepts that have been injected into the theory we are left with the concept that a hypothetical process exists where inanimate substances can gradually transmute generation by generation into any form of creature including mankind. We see that scripture advertises the idea with dust of the ground being formed into Adam or stones being raised into descendants of Abraham.
I agree that there are well deserved criticisms for how evolution is taught, I just think that when the bad secular teachings are removed that evolutionary theory isn't inherently incompatible with scripture (provided we are exploring a figurative interpretation for the creation accounts).