I'm sure you know these kinds of claims are nothing new. Nor are the claims about their widespread damage to society. When The X-Files was at its height, Richard Dawkins criticised the series for spreading unreason etc. And that actually was an entertainment show. But as William B. Davis said in relation to Dawkins' comments, where's the scientific evidence of that pernicious impact on society? That's a hypothesis to be tested.Most of the people I know or have encountered who watch these shows do so because they already lean towards the conclusions presented therein. Indeed, the people who thought that what The X-Files depicted was real didn't care that it was fiction or entertainment. In such cases, the show's themselves aren't convincing anyone. However, they do serve to provide a common touch point for the dismantling of beliefs in bigfoot, ancient aliens etc. They are showcases of just how poor the arguments are for anyone of even an undecided hue. Censuring or refusing to air such material would play into the hands of the people who spread these views. They already espouse a culture of persecution and assuage to varying degrees of explicitness that the 'mainstream' intellectuals are trying to stop the truth from being told. Letting them speak gives the world a living monument to the questionable claims and evidence that these theories use and demonstrates that there's nothing for real historians to fear. How are historians to push back? By pushing back through whatever means are available to them. There are series dedicated to picking apart such paranormal claims (albeit many fewer than peddle such claims). But that's beside the point. We live in an age when TV and the like are far from the only media that historians can use. Look at this blog itself: it facilitates the communication on challenges to 'ancient alien theory' and other pseudohistory. I've been blogging and participating on forums for years. That's pushing back.
I tend to agree with much of what you say (and Dawkins overdoes it sometimes), but honestly feel that these 'theories' get way too oxygen that only keeps them alive somewhere. They belong in obscure chatrooms, not international TV that somehow legitimises them. Still, as you say, we need to keep pushing back where we can. Although we really shouldn't have to.