Only if the GPG signing process stupidly relies on the SHA-1 hash. I.e. if it takes an unsigned commit and signs only its SHA-1 hash and then creates a new commit with GPG headers. If that's how it works, that is massively stupid and can be fixed without forcing SHA-256 as a git hash. Just have the signing calculate its own digest for its own purposes.
That digest can be the SHA-256; since the infrastructure is there for it, signing should use SHA-256 regardless of what hash is used by the repository for identifying and linking content.
> If that's how it works, that is massively stupid and can be fixed without forcing SHA-256 as a git hash.
I don't think it's massively stupid. Unless you want to re-hash the entire Merkle tree structure to sign your commit, you basically have to trust the hashes in the Merkle tree (or have a separate parallel Merkle tree) at some point in what you sign, which means you do have to trust the SHA-1 hashes. Otherwise even with a cryptographic signature you can always spoof at least the git repo history (e.g. even if you try to directly hash the entire contents of the current commit).
Re-hashing the entire Merkle tree structure seems prohibitively expensive to generate (even with a lot of caching) and pretty complicated for e.g. verifying a signature. Or you can do that incrementally, but then you're just generating a whole new parallel Merkle tree structure.
Regardless, at the end of the day, you need to trust the integrity of the Merkle tree structure. And you can either do that by trusting the hashes of the current Merkle tree, or you have to completely recreate a new one with more trustworthy hashes, in which case why not just use better hashes in your original tree?