The reason some people make their profile private is because they don’t see why anyone else should be allowed to look at their Summary / Activity pages, not because they don’t want people seeing their Armoury pages but, because there’s no granularity as to what you can make public / private, it’s an all or nothing thing.
However, it’s incredibly easy to see another player’s Armoury pages. Let’s use my Armoury Career pages as an example…
EU - https://eu.diablo3.com/en/profile/Meteorblade-2266/career
US - https://us.diablo3.com/en/profile/Meteorblade-2266/career
Asia - https://kr.diablo3.com/ko/profile/Meteorblade-2266/career
You’ll notice that in each of the three URLs, you can see my Battlenet ID, albeit that the separator in the URL is a dash rather than a hash. So, you could look at your own Career page, and then just type another player’s Battlenet ID into the URL to see their pages instead. If you hover your mouse over someone’s forum avatar and/or their posting name, your browser will show a preview URL that includes their Battlenet ID.