Home Pod Mini Set up Error 301003

I believe this error code is associated with this limitation mentioned in If you can’t set up HomePod - Apple Support:

• HomePod doesn't support public or subscription networks with sign-in requirements. These networks are often in places such as businesses, schools, dorms, apartments, hotels and shops. 

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I was having the same issue. Took me over a week to finally get it to set up. Even after consulting with two different people are Apple and getting no where. This is what I did and set up immediately. I opened my music app and just let it sit in the background. I deleted the room screen off the home app so it just displays the continue button. This is what I think actually worked. In apple’s recommendations they say to make sure the iCloud Keychain is on, I turned it off and after going back and trying the setup process again in set up with no issues what so ever. After the set up I just went back in and turned the keychain back on.

See if you can't set up HomePod.

I'm having issues with my 2 HomePod minis also. Worked great for a few weeks or so... now constant problems. They keep disconnecting from my wifi and HomeKit and will not setup properly. Now nothing! An Error Code 301003 comes up. I've been through all suggested solutions... first rebooting/re-starting everything. Then resetting the HomePod minis with no personalization. Then resetting the HomePod minis, wifi, bluetooth. Restarting my iPhone etc. Nothing. I now own 2 cool-looking paper weights that cost $99 each. I will abandon Apple HomeKit and move to other vendors and solutions... this is way too frustrating. I'm a former Apple employee (retail business team) and am proficient on Apple devices.