For whatever it's worth, I don't feel like I actually had to adapt my tastes at all in order to eat healthier. The main hurdle was figuring out how to prep in a way that's easy enough that I'll actually bother.
I wouldn't describe myself as actively adapting my tastes: I just ate better and eventually noticed my preferences shifting. I assume it's some combination of my brain getting more sensitive to the stimulus (of eg sugar), my gut changing, and my better diet reducing cravings.