There used to be plenty newspapers sponsored by wealthy industrialists; the latter would cover the former's gaps between the costs and the sales, the former would regularly push the latter's political agenda.
The "objective journalism" is really quite a late invention IIRC, about the times of WW2.
https://en.wikipedia.org/wiki/Journalistic_objectivity
"To give the news impartially, without fear or favor." — Adolph Ochs, 1858-1935
Objectivity is the default state of honest storytelling. If I ask what happened ? and somebody only tells the parts that suit an agenda, they have not informed me. The partisan press exists, because someone has a motive to deviate from the natural expectation of fair story telling and story recounting.
Already at the level of what stories are covered you have made choices about what's important or not.
Your newspaper not covering your neighbors lawsuit against the city against some issue because they find it to be "not important" is already a viewpoint-based choice
A newspaper presenting both sides on an issue (already simplifying on the "there are two sides to an issue" thing) is one thing. Do you also have to present expert commentary that says that one side is actually just entirely in bad faith? Do you write a story and then conclude "actually this doesn't matter" when that is the case?
There are plenty of descriptions that some people would describe as fair story telling and others would describe as a hit piece. Probably for any article on any controversial topic written in good faith you are likely able to find some people who would claim it's not.
I think it's important to acknowledge that even good faith journalism is filled with subjectivity. That doesn't mean one gives up, you just have to take into account the position of the people presenting information and roll with that.