Can you connect wirelessly an xbox one to a mac airport hdd?

Another suggestion I found, obtain the MAC address from your XBOX and see if you can add it to the AIRPORT to allow the connection to go through. I'm not sure where you do this on the AIRPORT but if it is blocking anything it could be this.

Before any think may be you can read something here :

support.xbox.com/.../multiplayer-connection-error-solution

So, if i understand, before, you are connected with wifi and now too. You can try to activ the NAT on AirPort Extreme with a computer which is connected with this network device.

1) If you use a MAC you have a procedure to access to your AirPort Extreme and activ the NAT in the parameters :

manuals.info.apple.com/.../airport_extreme_80211ac_setup.pdf

2) If you use Windows, you can read this to find IP address :
www.itworld.com/.../what-s-ip-address-airport-router

After, you tip this address in your web-browser and normally, you will access to your AirPort Extreme and try to find the NAT option.

But, when you have access at parameters to your AirPort Extreme i think the best solution for is to modify your AirPort Extreme into access point, not getaway etc. if it's possible in the parameter.

Please take a few minutes to read the questions
here, and answer them in your post. Thanks!

As long as the router the Xbox One is plugged into is the same as the one you are connecting to wirelessly then yes. You can do this, I use a Netgear and the Xbox One is cable connected to it and my Surface Pro, iPad and iPhone all see it through SmartGlass
as they connect through wirelessly to the Netgear router.

On the Xbox One, if you are having issues getting into multiplayer gaming with this router, it may be blocking Teredo tunnels. This is a setting that is left unchecked by default on this router.

To allow Teredo tunnels:

Open the AirPort Admin Utility. (It is installed in the Utilities folder in the Applications folder on a Macintosh computer, and in Start > All Programs > AirPort on computers using Windows.)

With the Utility open select your device from the menu on the left.

Select Advanced from the menu at the top.

Select the tab labeled IPv6 Firewall. (This tab will be visible only if the IPv6 Mode is set to Router or Tunnel and if the “Block incoming IPv6 connections” is checked)

Check the option to Allow Teredo tunnels.

Select Update. You can find this “Airport Utility" on a Mac or a iPad or iPhone app called airport utility.