steeldragons
Steeliest of the dragons
Ok. Sure. I'm game for a bit of mental experimentation. Let's seeee...I see. So it is not because of 5e PHB but because of your homebrew. This was my confussion. Thanks for clearing it up. Minor what if because I am interested in the way your world works.
Can someone from the Barbarian tribes not find out what a Druid is while adventuring?
Sure. I mean, they know what a druid is...they just kinda think of them as "wizards". Shamans are the goodly magic-users who deal with the totem spirits. Druids are the wandering wizardly guys who work with nature (which, obviously, the totem spirits are in charge of, so that's cool). Clerics and actual arcane magic-users are probably [since they don't really understand "Divine" or "Arcane" magic] dealing with strange/evil spirits or hateful demons. If someone can prove themselves trustworthy/honorable/good guys, then fine. But that will take some time to prove and within that time pretty much anyting that goes "wrong" is going to be the fault of you and your evil spirits.
For example a Barbarian that wanted to be a Shaman but was not allowed to by his family or tribe and then left the tribe to find his own way and then stumbled upon a Circle of Druids and decided to join?
Hmm. This has a lot of assumptions.
1) The druids would need to prove/believe that the barbarian was sincere and capable. The druids would have to offer him/her a place. The barbarian couldn't just "decide to join." Though the "proving yourself worthy" could be a fun set of tests/side quests.

2) If the barbarian "wanted to be a shaman" then I would probably just say "then why don't you play a shaman?" The shamans are "chosen" by the totem spirits, so the Gorunduun believe. No one is going to stop/argue someone from becoming a shaman (except the totem spirits, themselves). But,at the same time, one cannot be a shaman just because they "want to." NOW, this being a potential PC, I [as DM] would say "Sure. Absolutely, play a shaman." So if that was the actual concept: "My guys wants to be a shaman", then they would have not been a Barbarian [class] in the first place.
3) This also presumes that my world's Barbarian class is what you're looking at in the 5e PHB. It is not. It's...similar. It involves some of the same tricks. But it is not the class in the book.
4) If this is about "but I want a Druid who can Rage" then I would point you to my homebrew's "Berserker" theme...a necessary divorce from the "barbarian" class to allow for a class that is also a culture. Any class can be afflicted with Berserking. It probably doesn't do things exactly the way you want, but it's close.
I am not talking about level dipping but actually making a character that you could role play and be a little different. So my first few levels would be barbarian then I would switch and be a Druid that didn't forget were he came from.
So, being honest here, "not forgetting where I come from" reads to me as "justifying why I get to keep my Barbarian goodies"...a.k.a. why I get to have my cake and eat it too. Thus, I am inclined to say "no."
Now, if this is a "roleplaying character development thing" that's fine...great! Enjoy! You can start as barbarian for however many levels, switch to druid. You don't forget where you come from, but you have been spiritually [and metagame-wise] "reborn" [at 1st level, mind!] as a Druid.
So, no keeping most of the "barbarian goodies." Certain things that really wouldn't make sense to take away, like most of the cultural add-ons: skills, weapon prof's, ability bump, etc... you'd retain. Barbarian Class Features, like Danger Sense [since I just happen to have the PHB here with me at the moment and that's something both the PHB and Orea Barbarian have in common], no dice. You want to be a druid enough to change, that's cool. It's your character's story. Be the druid. There's probably not many, but Gorunduun human druids are certainly plausible.
Again, if this is about "But I want to be a druid who can rage" then it's not about roleplay and character development, it's about powergaming with a thin brightly colored candied coating ["but the 'why' of my background story..."] and no amount of background story is going to make me say "Oh, well in that case, a Druid/Barbarian is just fine then."
If you want "a druid who can rage", just say so. Then I say: 1) be a Druid. 2) take the Berserker theme. Optional 3) be a Gorunduun human if you want your character to be recognized/thought of, in the world, as a "barbarian." 4) Here's how all of that works. 5) Welcome to Orea. Have a ball.
In short [too late, I know], there is no reason you have to change/work outside of ["break"] the system [in this case, my homebrew system/setting and what is permitted there] just to "be a little different."