As a family that has the TV on a lot, I'd like to offer a different perspective of this. This answer works primarily for sports though, where you can ignore the TV for a while without missing much. If your family puts on a TV show where they have to pay attention, this isn't the answer for you.
My family and I have football on most of the day for most holidays. We don't have it on because we're riveted to each and every play, though; most of the time, we don't actually care that much about the game. Instead, we have it on because it gives us a conversational "meeting point".
For example, this Christmas, we had the Steelers-Texans game on (among others). For those who aren't football fans, it was pretty obvious this was a one-sided matchup, which usually translates into an uninteresting game. That didn't really matter though! None of us wanted to watch football in silence after all, we wanted an excuse to start up conversation. The Texans have a star defender, JJ Watt, who raised $37 million in relief for Hurricane Harvey, so we spent a good deal talking about that, about fundraising, about Houston's recovery after the hurricane, and so on. My brother's girlfriend lives in Wisconsin, where JJ Watt is from. She moved the conversation to Wisconsin in general, which led to its own long tangent! One of the Texans recovered from cancer and was playing yesterday. We obviously spoke a while about him too.
I'll concede that most of us enjoy talking about football itself, but most of our conversation didn't really involve football at all. In addition, if anyone suggested something besides watching football, we were quick to jump on it! My brother suggested playing Settlers of Catan, and 4 of us went to play that, while those uninterested kept watching. After our game, we reconvened and rejoined the conversation. That's why I describe the TV as a "meeting point". Any of us are happy to do something else, but barring that we have an easy option to gather together and talk.
But Lord Farquaad, I don't know anything about football! It's hard to jump into conversation!
I know, I felt the same way for a long time. I found learning a conversational amount about whatever they're watching goes a long way (I also ended up loving football, but your mileage may vary there). My brother's girlfriend doesn't care that much about football, but by keeping tabs on JJ Watt, a prominent player from her city, she was able to move the conversation to something she was interested in.
This is actually just a good IPS skill in general. You'll find that regardless of your family's interests, it will be much easier to jump into conversation if you're a little familiar with that area. It also makes it easier to identify if and when you should suggest another activity. If the game were tied with a minute to go when my brother suggested Settlers of Catan, noone would've joined him. Instead, he waited until one team (I won't say which) was up by a good amount, knowing we'd care less about the game.
All in all, I suggest you observe your family a little and see why they have the TV on. If they're giving it their undivided attention, you will have to suggest turning it off. If they're talking over it though, or willing to do other activities, join in on that! Suggest things they might like to do, and many are likely to join! Learn a little about what they're watching, and use that to move the conversation to things you'd like to talk about! They're using the TV as a social tool, you can too!