Are the viewers paying the operator? If not, I'm not sure you can really argue they're legally responsible for "encouraging" the operator. The operator could say, "I'm going to make another child abuse video for every million people that vote for Hillary Clinton", and no one would blame voters for "encouraging" him. Even if the operator has ads on the site, I don't think it's reasonable to call the viewers culpable--their financial contribution is unintentional, miniscule, and possibly negative if they used an ad-blocker.
For all we know, the "operator" was just showing a dump of things he found on an abandoned site five years ago, and was not involved at all in the production, and had no intention to be. Or perhaps he applied the principles of the MPAA and pirated for free as much material as he could, and put it on his website for free so as to try to get viewers to stop paying the producers and supporting their crimes.
(Which, by the way, is a strategy I would recommend law-enforcement pursue if they take their own arguments seriously. Spend federal money on servers hosting free, searchable torrents and direct downloads of CP; perhaps restrict it to material produced at least 20 years ago, and strip out or change any identifying metadata, so as to avoid any semblance of supporting or encouraging the producers of the materials.)
If you want to make the case that the viewers are liable for supporting the production of child abuse materials, that's a specific claim that you would have to prove in any individual case. By no means is it to be assumed.
What you mentioned was "encouraging its distribution", not "its production". Still, I can't imagine why the former would be rationally considered criminal except insofar as it contributes to the latter (notwithstanding rhetoric about "re-victimizing our children every time it is passed from one person to another"--which is completely absurd unless the viewers encounter the victims in real life and mistreat them in a way they wouldn't have if they didn't see the video, which seems outlandish--I doubt if it's even possible to track down the real-life identities of the victims most of the time).