I'm sure you're folks thought your music was garbage as well. Wash, rinse, repeat.
I don't listen to Taylor Swift, but as a girl Dad of three, I've certainly had it as background music in my home and car for about 10 years now.
This is what I know. She's incredibly hard working and creative and has been since she was about 12. She writes all her songs and her lyrics resonate with people of all ages (but young girls particularly). Her songs tell stories that are easy to understand. They just happen to be wrapped in a style of music that rubs some the wrong way.
I've actually been to one of her concerts (not by choice), and I will say this. She performs likes she's scared. Scared that she will disappoint someone. Scared that someone will see her as a fraud. She brings everything, every night. She's not inherently cool, hip, or sexy, so she makes up for it with grit and hard work.
Do I tire of seeing her every 2 mins when I'm trying to watch football? Sure, it's a bit much for my liking. Does it bother me that she goes to games as a fan of someone she clearly likes? Nah, IDGAF, I hope she enjoys ball as much as I do.