Drama, I'm of the same generation as your mom,(though there are differences) and maybe I can give you some insight into her concerns and how you might be able to get her to see RENT with you. I'm assuming that you are a fairly young teen, 14 - 16? If that's the case, she's worried about what lessons you're learning about sexuality from the media and the culture. She's afraid that you'll see the characters in RENT as glamorous and that you may want to be like them. She's afraid you'll make mistakes, perhaps mistakes that have profound consequences, such as becoming HIV positive, or getting pregnant. I don't know if you're a boy or a girl. She's afraid of your taking on adult responsibilities too soon.
You told her that the show is about "living life to the fullest." I can understand if she doesn't find that comforting, as it's coming from you.
Actually, the show is about a group of friends who are trying to survive and grow in difficult circumstances. There is sexual activity, but there is - and here is the more important theme - also selfless love, committment and hope. They still dream, and try to make their dreams come true even in the face of poverty and death. You might ask your mom to see the film with you and then talk to you about it - her concerns and yours. These themes are universal, and I guarantee she will understand these themes. Let her know that the action of the show takes place in the 1980's and the characters are also products of their time. The choices they make will not necessarily be the choices YOU make. Let her know that your desire to see the film is not a total rejection of the lessons she's tried to teach you. If you don't whine or brow-beat her, she may come around if you show her you are reasonable and responsible, too.
Good luck. I'm looking forward to seeing RENT myself.
"And the postman sighed as he scratched his head, you really rather thought she ought to be dead..."