Reflex:
But unless someone gives me a positive reason to reject my “absolutist” beliefs …
How about the fact that you are not infallible? That you do not know the absolute truth? Would that be in conflict with your cognitive stance?
… a genuine alternative to those beliefs …
These are two different things. I may find good reason to reject something that I held to be true but not have anything to replace it with. This is why philosophy can be destabilizing. It is only after I see that my former assumption is untenable that I begin to look for a more satisfactory alternative. The Platonic dialogues are aporetic. Many students of philosophy have experienced periods of confusion and doubt. The rug has been pulled out from under them. Some retreat and denounce philosophy, others are more comfortable with this and come to see it as a sign of progress.
The relativism to which you refer, "relative to other truths, other facts, other ideas," is arbitrary and gives you a compass that points to nowhere but yourself.
How is this arbitrary? Are we to disregard truths and facts and ideas? Knowingly or not, this is what you and everyone else does. It is what Morris describes, isn’t it?
The idea is one thing; the ideal-reality it points to is quite another.
The “ideal-reality” is just another idea, something you think must exist, something that must direct for otherwise we are directionless. You may be uncomfortable with that possibility but the truth is determined by we would prefer it to be.