It's not possible, no. Historians always have to interpret their evidence, and this is always subject to the historians' unique perspective, training, background, and skill.
This is, of course, no different than any other field. Scientists have to interpret their results, and these results are generated from experiments designed according to the researchers' subjective experience and judgment. By which I mean to say, subjectivilty is a fact of life that experts in all academic fields work with comfortably.
Even though we're never able to be truly objective, we do have tools and skills which allow for interpretations that are better or worse. Lack of objectivity doesn't mean there isn't such a thing as a wrong answer (we rely on evidence, and interpretations which ignore it are wrong). But it does mean there are often multiple right interpretations of the evidence, which result from each historian's unique perspective and skills. This is what makes the field so much fun: our subjectivity allows us to continually discover new ways to understand the past that previous historians didn't think of.
No. No matter how one might try, one will always have a level of sympathy for whatever is being studied. One can try to be as objective as possible, but true objectivity is almost impossible for Historians to achieve. Apart from myself, of course .......