From my macbook I can easily share albums "anyone can view" (and anybody with the link can see the album without loging in) BUT when I try to share the same way from my iPad or iPhone it does not work: the album is shown as shared "anyone can view" and the link is created but when I (or my client) open it, it is requesting a log-in.
I tried this myself just now, creating shared albums in both Lightroom desktop and also Lightroom Mobile on my iPhone, and after enabling Get Shareable Link, both my albums defaulted to Anyone Can View. I then was able to view both my shared albums in a browser and I confirmed I was not signed in. I also tried toggling share off and back on again, and every time I re-enabled Anyone Can view, my shares could be loaded by users who are not signed in.
Can you double check that Anyone Can View is actually set -- enable it, and then confirm the setting (click Done on LR Desktop or tap the checkmark on iOS). If you can still reproduce this, could you send me a direct message privately with an example shared album URL? I'll send you a direct message now to help us connect privately