Everything has a bias. Period. It's not a matter of things being "respectable" for confirming your own bias, it's a matter of not lazily labeling as "propaganda" things that don't.
I also tend to think it’s much more productive to categorise news sources as either “bona fide” - an earnest attempt to thoroughly research and report what you observe, as you observe it - versus “mala fides” - everything else.
As you say, there’s no such thing as unbiased reporting. Every paper has a world view - I’ll quite happily nail my colours to the humanist mast of a paper like the Guardian.
“One of the principal marks of an educated man is the fact that he does not take his opinions from newspapers -- not, at any rate, from the militant, crusading newspapers. On the contrary, his attitude toward them is almost always one of frank cynicism, with indifference as its mildest form and contempt as its commonest. He knows that they are constantly falling into false reasoning about the things within his personal knowledge, within the narrow circle of his special education, and so he assumes that they make the same, or even worse, errors about other things,whether intellectual or moral. This assumption, it may be said, is quite justified by the facts.”
Nice to scratch one big thing off my to do list