Neutrality is not objectivity. It is quite possible, and common, that being neutral between two positions entails being non-objective.
Objectivity means making the relevant facts clear, giving relevant interpretations and the reasons for these, and then also giving one’s interpretation of those facts, and then the reasons for that interpretation. These last two steps are important so that a person can evaluate what is presented better – this notion of objectivity is why, in some scientific journals, scientists disclose any possible conflicts of interest. In so doing, a reader may better evaluate what is presented.
So, if two people are debating, and one is engaging in propaganda and intentionally trying to obscure facts, while the other less so, then being neutral between the two debaters is not be to objective – rather, if being objective, one should point out the former debater’s obfuscations, even though this entails no longer being neutral.
What I find frustrating is the pretense of objectivity. This is found, often, in textbooks or other books intended for an academic audience, say. The authors often do not present their own views, cloaking these under the pretense of objectivity. Yet, it is precisely the opposite of objectivity to do so. I would much rather a textbook where the author states their views, and even argues extensively for them. To be non-objective, on the other hand, would be to intentionally distort or occlude relevant facts, omit important responses to a given position, and so on. None of this is incompatible with presenting one’s view. (The pretense of objectivity also often makes for more boring reading.)
Arguments, in terms of their actual merit, often gain considerably by being more objective – the arguer is forced to understand the relevant facts, the responses to various arguments, the counter-responses, and so on. (Rhetoric is another issue.)