Upon whom do the costs of cutting down a palm tree fall, which thieves climbed to burgle a neighbor's house: upon the owner of the palm tree, or upon the aggrieved neighbors?

Neighbors should recall the Quranic verses and Hadiths that encourage kindness to neighbors, and deal with overlooking and tolerance instead of contention. Regarding the palm tree that thieves climbed to the neighbor's house, there are two cases: First: If the palm tree is entirely within your property and has not extended to the neighbor's property, the neighbor does not have the right to demand its cutting unless there is apparent harm, such as the palm tree becoming a permanent ladder for thieves. If that is the case, then you must remove it or secure it, and the cost of cutting would be on the neighbor due to no aggression on your part. Second: If the palm tree is leaning or its branches have extended into the neighbor's property, the neighbor has the right to demand the removal of what has extended. If you do not do so, they have the right to remove it, and the cost of cutting would be on you to ward off the harm from your property.

It is preferable to reconcile and share the cost for the sake of goodwill.