I'm not sure how applying religion to this process is practical/useful.
Let's assume that morality and religion are the same thing.
Morality and science are separate domains - that's quite obvious. However, my argument goes one step further: morality encompasses science and science is subordinate it. Morality tells science what areas to explore while the opposite is not true: we cannot derive any morality from science or validate any religious claims with it.
...truth exists independently of any human or any sentient being.
Absolutely. The ultimate truth is external to our reality and is unreachable within it.