Same problem here. I don't have a firewall on my router so that's not the issue.
If I try to open the Home app it is forever stuck on the Loading Accessories and Scenes.
No amount of waiting shows me the Reset HomeKit button.
I signed into iCloud with my wife's account on my iPhone and everything worked immediately.
I could open the Home app and pairing the HomePod worked flawlessly. Therefore I can assume that there is nothing wrong with my iPhone and a full restore (as some recommended) wouldn't make any difference.
There seems to be something amiss with my iCloud account in connection with HomeKit but I have now way to reset it.
I downloaded a couple of random HomeKit apps and when trying to access HomeKit they both display this error: Cloud data sync in progress.
I logged into iCloud on an old iPod Touch with iOS 9 that has a Reset HomeKit option in the settings but this did nothing.
There is a long thread about this issue on the Apple Developer Forums but none of the answers helped me Home app stuck on Loading Home... screen | Apple Developer Forums
If I connect my iPhone to Xcode I can see messages like these in the console:
Feb 10 13:59:51 iPhone-X homed(HomeKitDaemon)[161] <Notice>: Answering incoming message kAddHomeRequestKey (321BB621-CFAB-4BB8-AFF2-7F3451084CFC) from client 'Home' that does expect a response with error Error Domain=HMErrorDomain Code=77 "(null)"
Any other ideas of what I can try?