You say she's a teenager but not how old - if she's 13 and living under your roof then that's different to her been 19 and living somewhere else.
Ultimately she has to make her own mind up - yes you can have conversations where you encourage her to think for herself but if if you come up against something she believes in then she will entrench and you'll make matters worse.
You catch more flies with jam than you do with vinegar.