Existentialism addresses this question directly. Morality and determinism do not have anything to do with one another, the one is a psychological fact, and the other is a physical theory. Freedom and responsibility are parts of the nature of humanity whether or not determinism forces us to alter their definitions or interpret them in arcane ways.
From Sartre's point of view, we do not have moral responsibility on the basis of any observed external reality, we have moral responsibility on the basis the nature of consciousness, which creates our need to remain authentically connected to our genuine emotional states or become incompatible with ourselves and end up either destructively uncomfortable or mentally ill. No physical fact makes anything morally acceptable.
For example, the argument for not oppressing gay folks is not that nature creates the inclination toward homosexual pairing. It also creates natural motives for rape and mass murder. Applying this notion that realities of neurology or physics determine your ethics is entirely a 'naturalistic fallacy'. Your ethics are the result of a psychology and cultural evolution, to demand that they reflect your physics is a pretense.
The generally accepted cultural argument that we must find acceptable what comes naturally is nonsense. It is easy to make, but it applies just as strongly to pedophilia and to narcissistic sociopaths committing violence for attention. And we just don't apply it there. (In fact, when we do and do not apply it shifts at our cultures' convenience. For instance, feminism is rolling back the 'boys will be boys' naturalistic argument that we require a certain level of rehearsed culturally-narcissistic sociopathy of those we intend to send to war, and thus must accept the social damage that results from traditionally prescribed male roles.)
What is really being applied is the Existentialist notion of authenticity itself. Inauthenticity is a personal cost, and if we wish to impose it on people socially, we need a reason. We can observe the fact that pretending not to be gay imposes a form of inauthenticity, and the social benefits, now that the population is already too high, do not offset it. That is totally different from pretending that the neurological facts dictate a policy of acceptance.