In Rivals of Catan a player can be forced to discard buildings. If a player chooses an Abbey, do they also lose their University (which has a dependency on an Abbey), or do they just lose the Abbey?
No, they only lose the first card.
There are no dependencies, only requirements that must be met in order to play the second card.
On Page 16 of the rules it states:
The Theme Sets introduce cards that have special requirements that must be met before you can play them. The requirements may vary significantly - such as requiring the trade advantage or requiring that another building must already be in your principality.
Once the card is played and the requirement is satisfied, the requirement has no further effect on play.