I think you know who they are. Still, I'll answer your question.
They're a small, fringe sect of ultra-Orthodox Judaism. Their size is minuscule within the Jewish world, which is saying something. They call themselves "true Jews" but even other anti-Zionist Jewish groups and individuals take issue with that...and a lot of things they do, even things unrelated to Israel.
They reject SECULAR Zionism, wanting the creation of Israel but under an unquestionably divine power. The fact that humans are involved with the creation of Israel, and that Israel isn't an theocracy like Iran or Saudi Arabia (except for Jews instead of Muslims), is what they really oppose. Their interpretation of religious law is strict in this regard, and makes no room for anything outside their narrow interpretation of what Judaism is. Other religious Jews are fine with secular elements and people, but for NK the objection to anything secular which is why they tend to not get along with other Jews.
As I've said, they're not a large community or even decently sized. So...why put them on tv? Their opinions, as far as Jews are concerned, are irrelevant and unrepresentative so they can only represent themselves. And NK does't hold too much power or influence so most people don't care... unless you fetishize them. Which is the role they oh so often play. A lot of people only bring them up because they want to push their Jewish identity against Israel and really wouldn't give a #$%^ about them otherwise. That's why biased outlets give them screen time whereas those without specific narratives pushing them ignore NK, recognizing them as something normally un-newsworthy.