Personally I think I've arrived at a place where I'm wary of Gell-Mann Amnesia both with the established sources, and with the conspiracy rabbit holes. I've seen both NYT and "alt" news say things that are straight-up incorrect about facts that I know from my own experience, in my own domains of knowledge, so I'm not going to trust either blindly. I'm left trying to piece together from various sources of different slants, at different points on the established/fringe spectrum. This is harder than taking a side, but I want to believe it's worth it.
Btw, I'm not trying to draw a simple equivalency here. "Thinking for yourself" isn't as easy as saying "both sides distort" and plotting a naive midpoint between extremes. You have to read everything critically.