the validators will just validate both sides of the split.
No they don't, since the two signatures they would make for different branches would get posted to the chain as evidence [1] and their stake (a minimum of 32 ETH) would get forfeited.
That's only in theory though, since the whole process depends on slashers running on the network, and currently nobody is daring to report anything with them lest it quickly become a political censorship issue within their community.