Thanks for the additional info. Your advice worked like a champ. It went just like you said with one modification. The washer and dryer only work on a 2.4GHz spectrum, so once I figured that out and moved the phone and machines to that wireless network, I was able to complete the setup. They connected to IPFire right away. No proxy issues. I was also able to move the phone back to the 5GHz connection and still control them.
FYI for any other Maytag users, the mobile app is shite, and doesn’t track with the instructions/words on the machine’s display. I also had to figure out how to clear the original wifi config on them before I could connect to the firewall (hold the “remote enable” button for 15 seconds). Once connected, you can control them remotely, but you have to enable that function each time you turn the machine on. That might be a decent security feature, but will probably get tiresome over time.