> It's just impossible to summarize any text without imparting some sort of value judgement on it, therefore "biasing" the text
Unfortunately, the above is nearly a cliché at this point. The phrase "value judgment" is insufficient because it occludes some important differences. To name just two that matter; there is a key difference between (1) a moral value judgment; (2) selection & summarization (often intended to improve information density for the intended audience).
For instance, imagine two non-partisan medical newsletters. Even if they have the same moral values (e.g. rooted in the Hippocratic Oath), they might have different assessments of what is more relevant for their audience. One could say both are "biased", but does doing so impart any functional information? I would rather say something like "Newsletter A is compromised of Editorial Board X with such-and-such a track record and is known for careful, long-form articles" or "Newsletter B is a one-person operation known for a prolific stream of hourly coverage." In this example, saying the newsletters differ in framing and intended audience is useful, but calling each "biased in different ways" is a throwaway comment (having low informational content in the Shannonian sense).
Personally, instead of saying "biased" I tend to ask questions like: (a) Who is their intended audience; (b) What attributes and qualities consistently shine through?; (c) How do they make money? (d) Is the publication/source transparent about their approach? (e) What is their track record about accuracy, separating commentary from factual claims, professional integrity, disclosure of conflicts of interest, level of intellectual honesty, epistemic standards, and corrections?