Given the extent to which political arguments rely on analogies to the past, I think it's unavoidable that history is going to be used for political purposes.
So, if our work is going to be politicized, the question becomes: how should we - as historians - react to the knowledge that someone is going to use what we write to make a political point? Should our writing be shaped by a consciousness of its political implications, or should we just 'tell the facts as they are,' and thereby absolve ourselves of responsibility for whatever political causes our facts are used to support?
There's an old, traditional school of history that's committed to positivism (telling things as they really are), and some of the more positivist historians will defend the a-political nature of what they do. Bryan Ward-Perkins, for example, wrote a book 10 years ago that argued that the Roman Empire was destroyed by uncivilized, barbaric immigrants. He ended the book with a caution to modern readers, urging them to be aware of the lessons we could learn from Rome's interactions with these immigrant peoples. This argument slides easily into modern political debates (immigrants will destroy civilization!), and in fact provided the precise framework for a recent anti-immigrant speech by a Tory government official (in which Syrian refugees were compared to the Huns, and Roman history was used as justification for Britain's refusal to open its borders).
Now, there's no indication that W-P is specifically anti-immigrant. In fact, I get the impression from his book that he wasn't trying to write a bald-faced apology for modern British racism. I think, in fact, that he's simply committed to following the evidence wherever it leads him - I saw him at a talk last week, and he questioned the speaker's heavy reliance on theory: is it possible, he asked, that theory might prevent us from reading the sources on their own terms? He's clearly someone who really just wants 'the facts'. Yet 'whatever [his] politics,' one critic of his book wrote, 'there can be no doubt that these works have been written sufficiently carelessly as to provide succour to far-right extremists.'
Whether or not Ward-Perkins actually set out to write a book that's ammunition for a particular political camp, that's what he did.
And that, I think, is why history is inherently political. Every time we spin a narrative about the past, we have to choose not only how to interpret 'the facts', but even more fundamentally which facts matter (and which don't), and even more fundamentally than that which things are facts. When we enter the archives, what we find depends partly on what we bring in with us: our assumptions about how the world works, about what's important, about what does and doesn't influence unfolding events. Part of that is our own personal politics. This is postmodernism meets history 101: everything we write says something about our own politics. Everything we write is political.
But everything we write also has an audience, and we - being intelligent people who study human societies for a living - should know that everything we write will be received as supporting one or another political position whether we intend it to or not. You don't have to be a Tory to write a book that supports letting immigrants drown in the English Chanel. You can be a nice, kind, inquisitive Oxford historian who just cares about setting the record straight and doesn't consider what kind of audience will really love his book, and how they will use it. But, I will say this without any hesitation, thinking about the political implications and uses to which our work will be put should be a fundamental consideration in how we frame our arguments. That is because one of the primary reasons people study the past is to help them understand their own time, and whether we like it or not, our writings are going to be used as political ammunition. So we need to be very aware of who we're arming, and with what.
What I'm not saying: I'm not suggesting that historians should twist the facts to support one particular political party (ie, ignoring all evidence for the good capitalism has done to further an anti-capitalist agenda). We have a moral responsibility to honesty, thoroughness, and fair-minded analysis of all available data. But at the end of the day, we each have to decide on a specific story to tell with the facts available, and that story will have a moral, whether we realize it or not. We should make sure that that moral message is crafted with the same honesty, integrity, and fair-mindedness as the rest of our work, and not act as though a 'factual' account of an event in the past doesn't also influence our audience's understanding of how they should act in the future.
History always has a lesson(s), and we need to be aware of how the lessons we write will be used in modern politics to make the world a better or worse place. If the stories we tell repress the voiceless, support the powerful, and reinforce stories of the superiority of white men or western culture, we can't be surprised (and certainly can't claim innocence) if Neo-Nazis start citing it as proof that they're right.
Some very good and thorough answers in this thread. While I cannot talk from a position of Historical authority there is something I would like to add:
It is easy to understand both that historical written sources have bias and that we, the reader have biases as well. What is very difficult however, is to comprehend just how thoroughly some biases are ingrained and to avoid the temptation to rephrase a source in our own terms.
One such example might be religiously-written sources. As a culture largely non-religious it can be hard to believe that the writer really thought like that. After all - he was so logical in everything else!
As another example, there are values in history that are not held in the same manner in modern cultures as previously. The notion of honour, for example, or duty or pride all have very different motivating meanings now versus the past.
Lastly, there is a temptation to write the history of an event as if the outcome was as obvious to the participants as it is to the historian. Thereby mistakes by the losing side become moments of obvious lunacy and moves by the winning side become inspired genius.
The point being that sometimes a "rational" interpretation of the sources can miss the truth as much as an intentionally biased one.