Acceptable for those that agree with them, sure. Ask somebody who does not.
And there is very little penalty for them for being inaccurate or biased if inaccuracy and bias aligns with biases of their audience, which are pretty clearly partisan. Do you know many Democrats that would stop reading NYT because they were hitting too hard on Trump or reported some news with anti-Republican bias? I don't think there are too many such people.
They aren't often though, because they stake their reputation on being accurate.
Bias is harmful, but I think the WaPo and NYT are a much more acceptable level of bias then say, Fox.