it is inevitable. Once someone brings up the problem of objectivity in historical study, someone is going to raise the charge of some sort of chaotic relativism, where there are no facts, just opinions, all of which are equally valid.
To be fair, sometimes the problem is caricatured this way. To be equally fair, this is always by its critics. Given enough time, this will always produce the charge of holocaust denial. Those pesky post-empiricists think that Holocaust denial is a legitimate historical stance since it can't be objectively dismissed (so Warren, The Past and It's Presenters, for example)
Let me stress this: This is nonsense. I am aware of no theorist who endorses such a position (Jenkins, who probably comes closest, is still well short of the mark).
Over on Vridar, Neil Godfrey waxes poetic about how much different other branches of history are. 99% of the time, as I've mentioned here and in comments on his blog, I think this is complete nonsense, and owes itself far more to Neil's romanticizing other ancient historians than their actual practice. There is one exception.
See, if you go ask a historian of Rome if he has created his history or discovered it in the evidence, he'll acknowledge that it is no doubt a little bit of both. It isn't going to be a strange question to him, and he isn't going to be offended by it, assuming he has been trained in the last fifty years or so.
Ask a New Testament historian that, and he's as likely to get offended at your suggestion that his work is purest eisegesis as he is to answer it. There are exceptions, of course. Crossan, for all his faults, is no reconstructionist. Allison, for all his strengths, is a lot closer to one. But, for example, NT Wright, for all his. . .well, NT Wrightness can scream "critical realism" all he wants. He's a modernist under a different hat.
The historian's work is purest eisegesis, or is at least in large part. The a posteriori, empiricist model of historical positivism is dead. Dead. Dead. Dead. Reconstructionists scarcely exist outside of the study of religion because theorists destroy them. They are such easy fodder that it's almost a cheap ploy to attack them. Yet there is still this curious conviction in the study of religion that we are extracting information, and heavens, never inserting it. Only in the study of religion is there a widespread conviction that historical Truth, capital T, is knowable.
I point this out because it is from Biblical Studies that I most often hear the caricaturized picture of the post-modern critic. They aren't alone, as my cite above bears out, but they are disproportionate.
Acknowledging the problem of objectivity is not an affirmation of abject relativism, and emphatically does not imply a rejection of factuality. The objectivity problem, in fact, has very little to do with whether or not factuality can exist in 99% of cases.
Here is an (I would suggest the) actual objectivity problem:
History is communicated in terms of narrative. That narrative is the product of the historian, and conforms to a model he had in mind before started, which is necessarily shaped by his context. That narrative is created around facts. it is not created instead of facts. That narrative is the product of the author. That doesn't mean that it can't be right, on the contrary, I think we are, in general, fairly good at conveying narrative that models the past. But it does mean that it is not found in the evidence, but in the observer. Our narrative of the holocaust cannot include denial of its occurrence and count itself equal, because it replaces facts, it doesn't simply reinterpret them.