I understand your reference to "objective" and "subjective" should be taken in the absolute sense (If I am wrong, my apologies).
I believe absolutely objective truth and absolutely subjective truth are not possible, therefore it is not something I desire, though one could argue in favor of desiring the impossible (that will be a later discussion, perhaps).
Let me offer my definition of "objective" and "subjective" such that both are defining limits of a particular topic: truth. I keep agreement with the general notion that what is objective (truth) is realized when it conforms to a set of standards or crietia that are in common within a particular community. Subjective (truth) is that which does not share the qualities of conforming to any external standard. Of course, this could be a great place to disagree with me, but I offer this definition in the hopes that what follows will justify my thinking.
Objective truth and subjective truth being defining limits are never realized in total. For example, nothing can ever be absolutely objective because it is an infinite regression of references to external standards to qualify. Because a propisition is true by a set of particualr standards, it might make it objectively true in that binary relationship, but it does not ensure the standards, themselves, are true in a similar fashion, etc... Godel's Proof and Carl Hemple's Confirmation Theory are good references here. Suffice it to say that any declaration that something is objectively true will reference an external standard that is held true
a priori and itself not subject to proof. Therefore, there is no ultimate truth that transcends reference to external critera which themselves, eventually, must rest on unproven criteria. So, it would be best to talk about
relative objective truth rather than
absolute objective truth. Something may be said to be more or less objective, but it would not be accurate to say that something is
absolutely objective; such an absolute, I have argued, is elusive.
So it is with subjective truth. It suffers a similar problem than absolute objective truth. In order for something to be absolutely subjective
it must be absent in conformity to any external standard. Typically, we arrive at a particular belief, at least initially, though a process of inductive thought. Such thought, of course, is governed by a set of assumptions as to what constitue truth and are set, consciously or not, as standards. Ultimately, the drive to justify those standards as being worthy so justify such an inductive "logic" present more infinite regressions in the search for an absolutely true standard by which to guide one's inductive thought process. Inductive reasoning like deductive reasoning reference a system of thought, itself, left as a series of axioms. Therefore, we can say something is relatively subjective, but never absolutely subjective.