I have recently realized that I have Bloodmoon above Tribunal in my load order. Is this a problem? I have heard that one must install Tribunal before Bloodmoon for it to function properly, but I'm using the Steam GotY edition, which installed the expansions along with the base game. If this is a problem, will I be able to simply move Tribunal up in the load order to solve it?

No, it's not a problem. At least I have never heard of any because of this, and it is common that they appear in that order.

But for peace of mind you can simply move Tribunal up if you like.