Which web server are you using in production for ASP.NET Core on a *nix server?
Use Kestrel, it's the way going forward. Refer to this: Change to IIS hosting model.
Does this mean it will work with say, Apache?
Yes and indeed that's the recommended approach. However, never expose Kestrel to outside world directly. Always put it behind a web server like nginx, IIS, HAProxy or Apache. More about Kestrel:
Some examples of using those reverse proxies: