All good work in History should be based off facts and evidence. If there's no or little evidence for a historical claim, it should be considered speculative and treated as such. When reading about a past event, there was a real event and a real set of circumstances, and discovering that reality should be the goal of the study. If evidence or lack thereof is glossed over or hand-waved for the sake of an agenda, or trying to make a point, it's bad practice. If people trust that conclusion, their conclusions will also be flawed as a result of this bad practice. In that sense, absolutely. historians should be objective. as for how to achieve it, it is a question of Discipline, not allowing bias to color your conclusions, always referring to evidence and having sources.

Here are my thoughts on the question, written a few months back.

In short, yes and no. 'Objectivity' or neutrality is important as a starting position (historians must weigh all the evidence even-handedly), but it's natural and desirable for historians to come to some sort of conclusion in the end. When all is done, we tell stories and we take sides -- whether we admit our preferences openly or not -- and that's always been at the heart of our discipline.

(It's true of the sciences, too: objectivity / replicability in methods, but an argument or story -- subjectivity -- framing it all.)