The GPL generally doesn't block a proprietary program from calling an open source one via a shell pipe. If it did, most commercial software running on a Linux system would run afoul of the GPL licensing of the core system commands (cp, ls, bash, etc.).

Furthermore, there are a number of more liberally-licensed binary-compatible reimplementations of Git available now (Grit and JGit spring to mind) that could be used as an alternate access layer, if you were less concerned with 100% compatibility with the latest Git features.