How does one deal with a dementia patient that watches cable news 24/7?

MJ1929, well said.   TV today doesn't offer much news other than the occasional building collapse, assassination, or weather catastrophe or juicy gossip that provides interest to override the apparently unlimited opinions so-called experts offer. 

Fortunately, there are good programs, especially the Masterpiece concerts, as well as  documentaries and craft programs, that do offer worthwhile entertainment and education.  I really, truly wish that Norm Abram's workshop series would be resurrected.    He is and was a master craftsman, and was very good at explaining how he chose and constructed his masterpieces.

I imagine she was bored out of her tree and got into the habit of sitting in front of the TV. Most shows are inane and with all the commercial breaks can be difficult to follow for someone with cognitive decline so news channels with their 30 second sound bites become the default, and because they repeat ad nauseum the information they provide sinks in. My advice is to break the habit by getting her off her duff and out of the house for a few days: go to the park for lunch or take her along when you pick up the groceries or run errands or whatever works and block the channels during this busy period.
The real challenge will be finding something to replace this habit.

You know, much of the issues with elderly parents are similar to those with small children. If something isn't good for a child to watch, we don't let them watch it.

My brother (now 63) was a Popeye addict at three years old, and he liked to emulate the big swinging slugs that Popeye would do to knock out the bad guys. As my folks were going to be welcoming me into the world soon, they didn't want my brother to knock out his new baby sister. The TV mysteriously "broke," and Popeye was history. The TV remained unrepaired for a year, and my brother calmed down immensely.

I have no issues with you turning on the parental controls. I wish some of those stations would disappear completely, because they're getting lots of people of all ages wound up unnecessarily and they aren't news stations -- they're commentary stations at best.

My own MIL doesn't watch it all day, but one of those channels has convinced her not to be vaccinated, and I have a real problem with that. It's her life, but she has based her opinion on no actual facts.