Further, I do not believe the two are diametrically opposed. All of history, all of personal experience, all of math, all of science, all of life - everything is a sweet combination of this pair, regardless of how narrow or broad you define them.
As far as how the objective relates to the subjective, I have found the following quite intriguing.
The deeper someone goes into any field of study, the more knowledge concerning that field they acquire. Obviously, this warehouse of knowledge is more objective than subjective. However, when those individuals begin to apply or use that knowledge, it seems as though the appropriation and application of it becomes more subjective.
Example - If you asked a college freshman English major what a participle was, they could tell you in perhaps 12 words or less. However, if you ask that same person 8-10 years later when they are completing their doctoral work on the use of adjectival participles in Shakespeare, they might begin their answer in a similar fashion. But... How they grasp the idea and employ the reality of "participle" will be drastically nuanced, and likely - far more fluid.
In my personal experience, the more I study the Bible, the more I read, the more knowledge I gain, the more I realize that there's more to know and the tougher it becomes for me to apply the existing knowledge I have. The greater the mass of the "objective" I attain, the more significant and fragile its "subjective" outworking becomes. I don't think this is merely a spiritual tension though.
A geologist will always become a better geologist if he keeps studying. But his becoming will never be only theoretical [mere study] or only functional [mere practice]. The marriage of these two - the theoretical and practical, the objective and the subjective - causes deeper pursuit of both.
The reason for this is that we are hard-wired for full fellowship without any partiality. We were not made to be befuddled by this seeming dichotomy. One day though, we will know fully and be fully known. There is no apparent contrast between objectivity and subjectivity in the forever flawless presence of God. "As it was in the beginning, so shall it be in the end" [Bob Marley] - redeemed man will be unhindered and be with God, like God, and for God... world without end.