Ok clearly there's a cultural thing at play here - I wouldn't have a clue that a particular channel has a particular leaning, and it seems there is a ridiculously biased channel I'm just not getting the scope of.
But I do still think OP was rude. I understand why better now, but I do still think it's rude behaviour - just as rude as OP's Aunt's behaviour.
Good etiquette for entertaining a guest in your home involves making your guests feel comfortable and welcome.
I think OP's dismissal of Aunt's request was abrupt and not necessary. I think that makes it rude, and clearly it affected aunt's relationship with OP or aunt would not have been colder to her later on.
OP didn't go into this with her eyes shut - she knew aunt was strongly keen on this channel and that the subject would come up. She decided that she wasn't going to put up with the channel in her own home - fair enough, not a problem, politeness doesn't demand that she does.
But there were other routes for her to take than just sitting and refusing to watch.
She could have chosen to take herself out of the situation the way I originally suggested, by giving aunt the remote and leaving her to it for a couple of hours.
She could have made light of the refusal by using some of the other suggestions people have made and changed the subject for an amicable agreement on what to watch.
OP might have been taking a stand - good for her and I applaud the sentiment - but that is politicising the discussion just as much as actually standing on a soapbox and denouncing the channel. By doing it, she is opening the door for Aunt to start picking at why the channel is banned - and I think Toots is right, aunt was trying to pick an argument. (Good for OP for not giving in to it btw) If she really wanted to avoid the politics involved, she would steer away from the channel using another reason or she would remove herself from the situation.
OP's stand was using Aunt's time as a guest to make a political/personal point - "I am not of that leaning, I hate that channel and you watched it on-stop when I was at yours".
It wasn't about entertaining aunt, finding a compromise or even standing up for herself. The time to stand up for herself was by asking aunt to change the channel when OP was a guest and seeing what transpired, or when aunt wanted to stay. OP didn't have to have aunt stay, knowing the subject was going to come up.