Apple ID page blocking Linux computers
The response from this user post in a related question was helpful. Specifically, apple is blocking the default user-agent string from Chrome and Firefox on Linux (at least Ubuntu based) computers. To confirm this, I did the following.

Change useragent on Chrome:


CTRL + SHIFT + I to open Chrome developer tools.
Click the 3 dots in the bottom right of Chrome developer tools:

Go to More tools > Network conditions
Scroll down to User agent and un-check Select automatically
Enter the following string Mozilla/5.0 (Macintosh; U; PPC Mac OS X;
fi-fi) AppleWebKit/420+ (KHTML, like Gecko) Safari/419.3
Enter the following in your browser https://appleid.apple.com


Change useragent on Firefox:


Enter about:config in the URL field and press enter (and accept
risk warning).
Enter useragent and press enter.
Look for general.useragent.override 


If you see it, right click it and select Modify and go to step 4.
If you don't see it, right click in empty area of page and choose New > String and then enter general.useragent.override as name and go to step 4.

Enter Mozilla/5.0 (Macintosh; U; PPC Mac OS X; fi-fi) AppleWebKit/420+ (KHTML, like Gecko) Safari/419.3 as value
Enter the following in your browser https://appleid.apple.com


Another way to test this in Chrome in Linux is follow steps 1-4 for Chrome useragent change. Next, instead of entering the example string above, select another useragent (Safari - Mac, Chrome - Mac, Chrome - Windows, etc) from the list. All those useragent's allow access to https://appleid.apple.com from Linux. 

Chrome on Windows 10 doesn't have a Linux option to choose from, so to test this from Windows, you can enter one of the following strings I pulled from a Linux machine with the latest updates:

Chrome/Linux
Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/72.0.3626.109 Safari/537.36

Firefox/Linux
Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:65.0) Gecko/20100101 Firefox/65.0

In my test this morning from a Windows 10 computer, using those useragent's in Chrome, attempts to https://appleid.apple.com resulted in a 502 bad Gateway.  That same test should work from a Mac but I don't have mine with me.

Test from Windows 10:


Some information about browser detection.