Need to be careful about which policy cards you are talking about. The Aesthetics card provides +100% adjacency bonus for Theater Square, so if you have that card in effect, whatever adjacency bonus your Theater Square receives is doubled. It does not double the adjacency bonus that Theater Squares might provide to neighboring districts and it does not double the yield of Theater Square buildings (amphitheaters, museums, etc.). So, in your example, if your Theater Square was getting, e.g., +2 adjacency bonus, the Aesthetics card would double that to +4, but the adjacency bonus that the neighboring Campus enjoys would not change. It works the same way for the other adjacency bonus cards. The Natural Philosophy policy provides +100% adjacency bonus for Campus, so if you have that card in effect, whatever adjacency bonus your Campus receives is doubled, but does not affect whatever adjacency bonus the Campus provides to neighboring districts. So, in your example, if the Campus was getting, e.g., +3 adjacency bonus, the Natural Philosophy card would double that to +6, but the adjacency bonus that the neighboring Theater Square enjoys would not change.
In addition to the adjacency bonus cards, there are policy cards that enhance the yield of Campus and Theater Square buildings, but do not affect adjacency bonuses. The Rationalism policy doubles the science yield from Campus buildings (library, university, etc.), but not the adjacency bonus of the Campus itself. Similarly, the Grand Opera policy doubles the culture yield from Theater Square buildings, but does not affect Theater Square adjacency bonuses.
