REPUTABLE academic publications go through a peer-review process, where others in the field try to replicate, challenge, refute and refine their thinking. That doesn't mean no one is ever wrong in those publications: it just means, as with the legitimate journalistic world, errors tend to get caught.
Good journalistic institutions (like the NYT, and, yes, the WaPo) try to catch their errors and be transparent about them.
Yes, they are both center left (and you can't claim that all of academia is -- that's way too broad and ignorant a brush) but that doesn't mean they're "left-wing ideological garbage".
So far, all your arguments against them have been this sort of unsubstantiated statement, offered because you believe it. That holds no water in a rational argument. Bring evidence. Offer alternate sources close to as credible as our national paper of record. Right now, you are making the argument that you don't accept those sources because they don't confirm your preconceptions -- an inherently irrational, ANTI-rational argument.