There’s no security reason to do so as forks would be permanently divergent. So all it would do is change a hard fork choice incentive from ‘what I prefer’ to ‘what I think the majority is going to prefer’ and (in practice) prevent the existence of a minority fork.
In addition it could potentially lead to a stall in the network at a (controversial) fork time as validators could prefer to pay an offline penalty just to see what fork the remaining majority chooses.
For these reasons I don’t think deposits should be slashed across hard forks. Are they going to?