Posts not showing in correct Alphabetical or ID order when using get_posts / orderby but only on production server

It would be atypical for server configuration to have a direct impact on posts query, short of SQL explicitly misbehaving. Which would be quite an edge case.

The much more common case would be some code attaching to query filters for its purposes and not being precise enough to target just the queries it needs to. Issue being specific to front end alone seems to point in this direction as well.

In either case the troubleshooting would involve digging down to actual SQL queries being generated and executed. At some stage there would either be discrepancy between correct/wrong environment or you would be able to exclude SQL and move on to troubleshooting PHP side of it.