Goedel was working in logical systems. It would be an extrapolation to infer something from his theorems beyond that.
The implication of Godel’s theorems is that scientists are just as subject to faith as non-scientists. Indeed, the renowned atheist Bertrand Russel was so shaken up by this fact that he lamented “I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than anywhere...But after some twenty years of arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.”
Again, in the ultimate sense, science requires FAITH. Therefore science and faith ARE NOT strictly incompatible.