I've spent way too long thinking about how to respond to this thread. So I've made an unscientific television spectrum for reference:

Active: You're fully engaged with a show, and have no distractions.

Mostly Active: You'll glance at your phone every once in a while, maybe to see what else an actor was in, but you largely pay attention to what you're watching.

Neutral: Split screen viewing. Let's say you're fishing in World of Warcraft while watching a show, or you're constantly glancing at your phone.

Mostly Passive: You have a sitcom rerun on in the background while you're cooking dinner or cleaning.

Passive: You keep the TV on because it gives the illusion you have company over, even if you can't hear it and you're sleeping on the other side of the house.
If you make plans with someone to watch a show or movie, and you put in less than Mostly Active viewing, you might come off as disrespectful to the person who made plans with you. Constantly glancing at something else heavily gives off the impression you don't want to be there.

If you watch a show Neutrally but post in online forums under the pretense of being an Active watcher, you come off as someone who's just watching the show for cultural brownie points so you can stay active in your friend's conversations.

If you have an Active interest in a show but you give it Neutral attention or lower, you're doing yourself a disservice by essentially being half-interested in something you want to enjoy.

For me personally:

If I'm watching a show for just my own interest, I watch it Actively. I treat it like a movie theater where I want to digest everything that's happening.

If I'm watching a show with family, I will be either Active or Mostly Active. Especially if you don't pick the movie, it can be helpful to google something on the fly, especially if your movie party doubles as trivia.

As noted, the only time I'll be a Mostly Passive watcher is if I'm cooking or folding laundry and I put on something inconsequential.

I'm never a Neutral or Passive watcher. I'm the type of person who has to be fully interested in what I'm doing, outside of chores. I have way too many hobbies and interests to either be half-interested or non-interested in what I'm doing.

As the great philosopher king Harvey Danger would say: If you're bored than you're boring.