My work is entirely grant funded and to my knowledge, none of it comes from the government— at least not directly. I'm positive that some of those private non-profits receive government assistance to some extent for operating expenses and whatnot, but the funds themselves are not tax-sourced.

Beyond that, governments fund libraries and archives at every level and they deliberately have all sorts of collections, from completely benign to completely odious. Funding a deliberately sensationalist aggregator and monger of violence would be plainly obnoxious, but appropriately managed archives are in the public's best interest. Probably even more so for controversial content. I'm not sure how this would be any different.