Thanks. I decided against having commit messages automatically close stuff on the tracker because:
1) Commits may need further review first
2) ... especially if commits are being done in merge requests, it's not clear if/how/when the tracker should be updated
3) The push_bugfix script we have now does a good job of keeping Mantis and GitLab integrated for day-to-day bug fixes pushed directly
4) It's another point of failure (maybe the integration will break and nobody will know how to fix it / it may be abandoned)

I do see value in an integration, but I don't think the pros outweigh the cons.