You asked a very good question! Well, what does this phrase, "sophisticated palate"mean?
Let's review these two words closely.
The word sophisticated refers to a clever, modern (up-to-date), well cultured view or approach.
The word palate, unfortunately, has more than one meaning. However, it is understood that in this sentence it refers to taste/preference. (None of the other meanings make sense due to the context)
Ok. In summary, the phrase sophisticated palate means a "modern, well cultured preference"
Feel free to contact me if you have any other questions?