I don't understand why you're treating this as a partisan issue. Fake news affects every political affiliation, and it isn't limited to political issues. I don't want incorrect information that agrees with my point of view any more than incorrect information that agrees with it.

As for how they'd decide what websites to block or put a warning in front of, that seems fairly straightforward. Have a committee that represents different demographics, and require a unanimous vote to take action against a site.