Those ethics were created from within a theistic worldview, they weren't born from reason. Adopting the ethics of a religious culture while denying the underlying assumptions is pretty unreasonable.
Why is that unreasonable? I've "adopted" the basic idea of Newton's gravity but deny the fundamental assumptions regarding the flat spacetime and "gravity as just another force" because general relativity showed those to be incorrect.
Animals behave ethically/morally and they have no religion.
It's possible that ethics were first written within a theistic context but that has no bearing on how they were created.
In many case, they were both; the existence of a theistic worldview does not prevent the application of reason.
> Adopting the ethics of a religious culture while denying the underlying assumptions is pretty unreasonable.
But we do adopt the relevant foundational assumptions, just not the irrelevant ones, where the conclusions are shared.
Of course, the conclusions are often different, because post-Enlightenment society often rejects substantive, morally significant elements of its precursors (in some cases, pre-existing religions have adapted to this and adopted, in whole or in part, Enlightenment values as well.)
Why? Are you saying that just because Islam stresses peace, hospitality, and philanthropy, that one cannot be peaceful, hospitable, and philanthropic without reasonably adopting Islam?
Furthermore, let's suppose a theologian - for the sake of example, let's say a christian one - insists that I am really a christian, on account of my ethical positions. Well, OK, but if that so, then it follows that being a christian does not involve believing in the Trinity, or that Christ is the son of God, or that God created the universe... in fact, that it does not involve anything beyond holding certain ethical positions, and that christianity is identical with secular humanism!
Of course, it is rare to find an avowed christian who follows this line of thinking to its logical conclusion. Motte-and-bailey argumentation [1] is rampant in theological thinking.