Listen to other shit on the radio. Demi Lovato makes Taylor Swift sound like Roberta Flack and the Beatles rolled in one. I liked the 1989 album, I think it could have been shorter but the sales don't lie.
Her shows are also amazing, her clothes are incredible and she's really beautiful. My big problem with her is her lyrics which I find a bit limited but I think people relate to how literal they are. She has a sense of humor about herself, she's unpretentious. The character she portrays is consistent and that makes her relatable. Her music is polished and seems more effortful than other big artists right now, like Drake or whatever.
It's pop music. Approach it with an open mind and learn about your fellow girls. I'd rather listen to her than the Turtles or the Monkees or something.
More than that, she represents the aspirations of like, millions of young women. I refuse to believe I can't relate to young women, so I refuse to be bewildered by Taylor Swift. Plus, she's tall.