Are chosen-prefix collisions for SHA-1 a major threat? GPG signing of Git commit tags relies on the collision resistance of SHA-1, which is weak.  However, the attacker does not get to choose the prefix.  How much does this translate to an actual vulnerability?
This is the same issue as with MD5, so you can search for attacks on that scheme.

An attacker can create executables that can do one thing during testing and another during deployment by replacing one file by another. As the signature doesn't change, the files in the repository would still validate. If you have a changed file then it is pretty easy to execute an entirely different code path when an application is run.

You would have to analyze the entire (sub-)system to see the impact of such a vulnerability on the system itself. I'd say that a well maintained Git repository isn't as vulnerable as e.g. GPG. It's probably not that easy to simply replace files that are already within a Git repository (but you'd better ask a Git expert instead).

In general signature generation and validation through message digest values are most vulnerable to attacks on the hash functions.