I mean, the one word answer to this question is "Branson" but really, let's say we were to put this what if to the test. The first thing there'd need to be is a decent POD and I think I have one. See, the comparisons of Taylor Swift and Miley Cyrus are not without merit, both started in country, though it was always with more pop leanings. Both released albums in 2010 (Swift's Speak Now and Cyrus' Can't Be Tamed) which introduced their new sound and new images as Swift began her slow transition into pop idol while Cyrus began her move to her more mature image.
So, the POD that keeps Swift in the country camp is Cyrus opting instead to go country after Hannah Montana runs its course. In place of "The Climb" the big hit off the movie is "Goodbye" a slower acoustic ballad written with idea of being a break-up song but also a way of saying goodbye to the Hannah Montana fanbase with the hopes that they'll stay with her as she makes the move from pop to country. Cyrus was still popular among a big demographic at the time, so while the plausibility is suspect (but when has that ever stopped me?) the singles success of "Goodbye" influences not only Cyrus' next album (Back to Nashville) but also convinces Taylor to stick to country, reworking Speak Now to better match the genre.
Parton, I imagine, would be a big influence for both going forward since she's one of the biggest female names in country (and being Miley's godmother doesn't hurt) and while the fanbases wouldn't be keen on each other, I imagine Miley and Taylor maintain a more friendly rivalry (a scenario I imagine is Miley playing the titular temptress in the video for Taylor Swift's cover of "Jolene")