⭐ Merited by vapourminer (1)
Instinctively, I would say that chain splits present no prune-specific vulnerabilities; even in the extreme case that the split is so far towards the root that it can't be reached from a pruned node's partial branches, there's no risk of false verification. In any case, chain splits are so rare and contentious that it would be prudent to revalidate from scratch after each one, pruned node or not.
They are not that rare, but in general in bitcoin are limited to one or sometimes two blocks and so don't pose an issue to pruned nodes. This changes if we adopt blocks which are gigabytes in size. The scam coin BSV, for example, experiences frequent chain splits, some over 100 blocks long. And verifying from scratch every time when their blockchain is over 8 TB in size is no small task if your node is pruned and you have to redownload from scratch.Perhaps you mean local chain reorganisations, not actual forks? A node may indeed discover a new, longer chain, orphaning previous blocks, but I don't see how this is prune-specific (given reasonable pruning parameters).
A chain reorg is a fork. And if the fork happens from a block your node has already pruned, then it will be unable to verify the new chain.I'm sure you don't really mean this 
You do if you want to do it securely, privately, and be based on verification rather than trust. If you are not running a wallet with data from your own node, then you are running it with data from someone else's node.