[SilverWolf]

I recently discovered that Kodi has a built-in web interface. For no particular reason, I set it up with my own local HTTPS certificate. (: Of course, this means any other device that wants to use HTTPS with the web interface gets a certificate error.

So I tried accessing Kodi with plain HTTP, but that says "the connection was reset".

Can I support HTTPS for those who want it, but leave plain HTTP available for devices that don't have the certificate?

[wsnipex]

that's currently not possible with the built in webserver. Its either https or http.
You can however put a reverse proxy (apache, nginx, haproxy,...) in front of kodi that handles both.