Yes, there are declinable quests on the app and PC version, but it can be confusing because right now you are looking at 3 questlines.
1. Event "Summer Mermaids" quests. These are not declinable and must be played in order.
2. Regular storyline quests. These are always there and must be played in order. They are usually not declinable though when you reach the end of a chapter you will be able to decline the ones you haven't done to catch up.
3. Regular "cyclable" quests. These are also always there and they are always declinable. Click on the quest to open it and click "cancel" to move to the next one. There are just a small handful of these that will loop round and round so you can just pick the one you need, effectively.