I didn't say it was "unrealistic", I said it was an "anti-realist" view. Surely some one with a philosophy background knows what "anti-realism", in contradistinction to "realism."
Also, I don't think you have to espouse the kind of epistemological anti-realism (or the scientific instrumentalism implied). You could go for a critical realist (cf. Popper, Musgrave) view, which is realist but fallibilist. That is, you can maintain that there is a world "out there", states of affairs that are the case even if unknown or unknowable, propositions that are true or false regardless of our beliefs regarding said propositions while also maintaining that we can never have absolutely certain knowledge.
To be honest, I think this is your view at times. You say "Just that they cannot be known." And the "they", I assume, are the states or affairs or propositions to which I referred.
All this is not to say that anti-realism or instrumentalism or idealism is not a live option. Some philosophers of science and epistemologists do espouse such views. But the opposite is also true: Many philosophers or science and epistemologists fight on the side of critical realism, against more post-modern, relativist tendencies.
As it happens, by the way, we have similar backgrounds. My PhD. is in cognitive psychology and philosophy (specializing in epistemology).