There are no neutral news sources in the United States. The Pew Research Center made this graphic based on polling:
From it we can see that exactly one organization was more trusted than distrusted by every ideological grouping, The Wall Street Journal. And while the Wall Street Journal may not be liberal/conservative biased, it is business biased. It is pro-business all the time.
Seven more sources were more trusted by conservatives than liberals: The Blaze; Fox News; Breitbart; The Drudge Report; The Sean Hannity Show; The Glenn Beck Program; The Rush Limbaugh Show. And three of those are just shows on a larger network, not networks in their own right. Four sources managed to be equally distrusted and trusted by consistent conservatives: The Economist; the BBC; Google News; The Guardian. Buzzfeed is distrusted by everyone. The other twenty-three are more distrusted than trusted by consistent conservatives and more trusted than distrusted by consistent liberals.
There are no centrist sources distrusted by both consistent liberals and conservatives but trusted by those more in the center. The Wall Street Journal and Buzzfeed come closest, but I wouldn't describe either of them as unbiased.
It's noteworthy that three of the four organizations who are never more distrusted than trusted by anyone are foreign. This may mean that consistent conservatives simply aren't that familiar with the BBC, the Economist, and the Guardian, so they haven't formed a negative opinion.
Part of the problem here is that even the international sources still have their internal biases. The BBC reporters don't have to choose between Republicans and Democrats. But they do still have their own biases. For example, every BBC employee in the United Kingdom has government provided healthcare. This gives them a somewhat slanted view of any US healthcare discussion.
You could try watching Fox News. Shepard Smith Reporting and Fox News Sunday are, to my view, somewhat liberal slanted. If you thought that CNN was neutral until 2017, this might appear neutral to you. Of course, this would involve skipping most of the other shows, particularly the evening opinion shows.
The closest US sources to the BBC would be ABC News and Google News. Google News has the same pattern of trust, but it's just a news aggregator. It doesn't have TV shows. ABC News does, but it is more distrusted than trusted by consistent conservatives (not about equal like the BBC and Google News). This may mean that it is better known among consistent conservatives. It would not be surprising if the group that doesn't know enough to have an opinion would have a negative opinion if they knew more.
This graphic is from 2014. It might be interesting to see how these responses have shifted since. What would the responses look like in 2019? From reports of the viewership numbers, it sounds like you aren't the only one who has lost trust in CNN.