Boba Fett Never Learned The Mandalore Way
There is room for fan theories to spin an explanation for Jango Fett being dismissed by Mandalore. The Clone Wars may have introduced the fact from George Lucas' direct input, but with his leading role in the Star Wars lore no longer a given, the reason for Jango's exclusion can be revealed at a later date. The same goes for how he came to own his Mandalorian uniform, if he didn't acquire it through traditional rite of passage. And while we're at it: no, Boba Fett's armor isn't Jango Fett's either.
On the one hand, Jango being a true Mandalorian wouldn't actually make Boba one by default. In the version of Mandalore explored in the now-Legends comics, novels, and video games, the culture wasn't like most in the Star Wars galaxy (or our own). If a man, woman, or any other being wanted to become a Mandalorian, they could--no matter what family, planet, or species they came from. So the explanation for Boba Fett not being Mandalorian is even simpler, because... he never became one.
Boba Fett Became an Outlaw, Not a Mandalorian
While fans can assume that Jango passed on some of his culture and Mandalorian ways to his "son" before he was killed, Boba Fett was forced to find his own path. But instead of taking a step into the Mandalorian way of life, Boba Fett took up with cutthroat bounty hunters and hired guns, instead (a childhood chronicled in Clone Wars). For George Lucas, that might actually be the life and legacy that Boba was meant to follow, since Jango never comes across as 'heroic' in the films. So we suppose there is some poetry in Boba actually growing up to become "a common bounty hunter" just like father. And the kind of killer that true Mandalorians, like the one now getting his own Star Wars TV show, would see as an imposter in a more honorable warrior's armor.
At their best, the Mandalorians are a a strong, intelligent, and honorable re-imagining of the iconic gunslingers, samurai, or sellswords of modern legend. The code of honor that dictated those ways of life also shaped the Mandalorian way. And if you believe the rumored plot of The Mandalorian TV show, the new hero may be on his own mission to restore those very values to the Mandalore of the Star Wars future. It's an incredibly promising corner of the Star Wars universe to explore, but one that fans should recognize has absolutely no connection to the bounty hunter Fetts whatsoever.
These questions and subverted expectations would possibly have been addressed in the now-canceled Boba Fett origin movie, or possibly even in the long-canceled Star Wars 1313 video game, also starring a young Boba Fett. With two down, fans must now hope that The Mandalorian TV show can offer some insight or fuel for fan theories... and pray that a third strike won't mean the end of Boba Fett's legacy altogether.