You mention "sound" in your title and "rational" in your question. "Soundness" generally refers to an argument being valid and having true premises. "Rational" can mean many different things including but not limited to (a) valid in form and (b) what a reasonable person would believe. I'm going to skip over the problems about parsing whether such a view is rational (you seem to presuppose that it is not in how you structure your question, so this indicates a particular definition of rationality probably closer to (b) where (b) has some relation to a set of core beliefs about human evolution as it relates to society). Things get even cloudier when you add the term "objective."
I think there's an Achilles' Heel in the position that you present which you should consider. Consider the following:
(1) Our thoughts in ethics are products of human biological evolution
This by itself proves nothing.
You need to add something like:
(IR) Every thought that is a product of human biological evolution is "irrational."
This would give you your desired conclusion: Therefore these thoughts are "irrational" / "not objective" / "unsound"
The problem with (IR) though is that it seems like it would apply to any thought. E.g.,
(2) Our thoughts that the sun orbits the earth are products of human biological evolution
By (IR), they are "irrational" "not objective".
Obviously you see the problem with (IR) as you qualify by adding "just a bi-product ... of evolution" and "not scientific". So you seem to be saying IR':
(IR') Every thought that is just a product of human biological evolution is "irrational."
But the revised (IR') opens problems in two directions:
(1) What makes something just such a product if not that it is arbitrary rather than mapping onto the world? If so, then it seems we should move to (IR''): Every thought that is arbitrary is "irrational". But doing so unlinks the science.
(2) Why should scientific thoughts be privileged on such an analysis? any such answer seems like it will have to appeal to some link to reality which will always be mediated by our grasp of reality which will always be a product of our biological evolution. (In other words, the trust we put in "science" is circularly built on already trusting the basis for science in our thoughts). Thus, it's not really clear how (IR') is better than (IR) since we seem to be smuggling the benefits in without proving why we have a right to distinguish types of thoughts relative to their biological and evolution origins.