Let us say that I claim I know that there is a God. You then check and determine that I am subjective. I.e. I believe I know that there is a God, but I don't know.
Can I do that? Have I done so? Well, yes, I have subjectively claimed an objective fact. Is it then a fact, that I have subjectively claimed an objective fact?
Well, that depends on how you view facts. One version of fact is this: an actual occurrence. Is it an actual occurrence, that some people subjectively claim something as objective, when it is subjective? Well, yes to me it is.
So when I done something subjectively, I am doing an actual occurrence. Now if you only view facts as being objective, then you run into the fact, that you only view facts as being objective, is an actual subjective occurrence, because it is a cognitive process in you.
So every time we play this game of objective, it is pointless, if what is going on, is subjective in part.