Because it is a new invention for the show
This answer will answer any question of the same nature of 'why did this Mandalorian not mind showing their face?' and that's because it's simply a new invention of the show.
In Star Wars Rebels, most of the Mandalorians in the show never wear their helmet outside of combat. The same holds true for pre-Disney takeover legacy content like The Old Republic, where the Mandalorians took a far bigger role.
So out-of-universe the reason that Jango Fett was perfectly okay with showing his face is because nobody had decided yet at that time that Mandalorians don't show their faces.
The in-universe reason is anybody's best guess. Perhaps the Mandalorians adapted an ancient custom of never revealing their face after the Clone Wars because of the Empire, or perhaps this particular branch of Mandalorians has always stuck to their "ancient customs". (Which mind you, are still newly made up, because the ancient Mandalorians in the Old Republic Era also show their faces on a regular basis and the Mandalorian series is the first time this helmet-must-be-worn thing has come up.)
And because he's been retconned as "not a Mandalorian"
And, apparently, new Disney canon has retconned Jango Fett to not be a Mandalorian, even though the old lore established that he was a Mandalorian. So if you want to go by pure new Disney canon, he was never restricted because he wasn't a true Mandalorian, but that won't help if you ask the same question about any other old Mandalorian that showed their face.