I have no problem with assertions that there's an objective reality. That seems very plausible to me in fact. I would certainly have a problem with someone denying there's an objective reality.
What I get concerned about is when people say we assess truth by comparing it to objective reality. I see no reason to think this at all. It seems to me we judge truth by comparing statements to our subjective realities. I can't see how it could be any other way. We also take comfort in the observation that all of our subjective realities seem to be pretty similar, such that we can nail down a lot that we're all pretty sure of.
I also think that if there is an objective reality out there our best hope is to triangulate it with a bunch of subjective realities. So we take our (always mediated) view of the world and take it to the town square and argue about it with other people who have their own mediated views of the world.
And that seems to do pretty well.
So knowledge is mediated, it is socially constructed, it helps us navigate our world, it is meaningful insofar as it does all those things but it is not obtained by direct comparison with objective reality, which we're not capable of.
This, it seems to me, is what we mean whenever we say we "know" something.
So when I say I "know" all of this I am saying that based on my testing of this idea against what I subjectively experience about the world around me, this idea performs astoundingly well. In addition, while talk of truth being some sort of correspondence with an "objective reality" sounds familiar and inviting and even intuitive to the ears of a guy that sprang from essentially European culture as it existed post-Plato (who knows how my barbarian anscestors thought about these things - someone presumably, but not me) - that sort of talk doesn't seem to reflect what I actually see people doing.
So I assume it's mostly pillow talk. It puts us at ease so that we can enjoy all the charms and wiles that Western civilization has to offer (and it offers a great deal).
But really, everyone knows that pillow talk is just a way of priming things and setting the mood.
There doesn't seem to be any good reason to believe we compare claims to objective reality, at least not in my experience.