This question was posed in one of my local groups. There was someone who posted a video titled the with the same question where he advises to just do what you want if you vibe with an Orisha. My answer covers a few things layered in that question.
You don't have to be initiated to work with Orisha. Orisha, at is core is Nature, so it's fine to make prayers, sing, dance, and offerings in nature and with a pure heart. No one owns Orisha. I also don't think everyone needs to be initiated period. Some initiated folks are the craziest around but because they had the money, they were allowed to. Now, that does not mean that it's cool to go make up your own Orisha priesthoods and representing yourself as a priest of Orisha nor does it mean that there is no purpose or need for any formal initiation. The rites are ancient and should be respected.
That said, I think there is a misunderstanding of what initiation is and is not. Initiation is not the right to work with an Orisha. Initiation is a commitment to a path aligned with your destiny. It is a huge responsibility. It is a covenant with nature and one that is binding. Orisha are also not chosen arbitrarily or just because you like this Orisha or that and feel a vibe with an Orisha so you should start making up your own stuff for the Orisha. . That is some European stuff that says it's ok to do whatever you want regardless of consequences and screw what the divine calls for... It's all about me. It's all Ego. We use divination to determine your path because divination is coming from a place beyond the Ego and into the soul level of existing. Divination is guided by your Ori... Your divine self..that knows the plan for your life.
A remarkable example of this is a brotha I did a reading for 20 or so years ago. I was in the Kemetian tradition but the energies are the same. He loved Herukuti...the equivalent to Ogun... Fire, battle...the warrior.. He asked me what his incarnation objective was. The oracle said Auset...the equivalent of Yemaya or Olokun. Watery, emotions, nurturing. That brotha cussed me out 4 ways from Sunday...because he was sure that he was supposed to be a warrior and he couldn't fathom that he would need to work with feminine energy. Years later, he got a reading in Chicago. Their readings told him Olokun was who crowned him. He went on to be initiated to the mysteries of Olokun. He apologized when we met up again and that brotha was soooooo different and peaceful and humble, I was floored! It it spoke to what the purpose of initiation and ones "Orisha" is.... His destiny was in peace, not in war...Olokun crowned him because that is what he needed for balance...and ultimately wholeness. Had he continued to follow the path he felt drawn to... The path his ego wanted...He would have been way off base and working against himself. Working against yourself is like swimming with weights on upstream.... It means a lot of things just won't flow right..go right... Because you are out of alignment. So that is first when it come to how an Orisha and Why and Orisha is determined.
Now as mentioned in another article, we don't having crowning Orisha in traditional Ifa. We focus on your Ori. Anyone can have an Ori altar... It's the focal point. Anyone can receive an Ori pot ...or an Egun pot for that matter. That is what I recomend for most people. It doesn't require initiation. That is the basis of our altar.. Pots...womb portals that bridge worlds. Egun are your ancestors... No one can take them away from you.. Before Orisha there is Ori..Your greatest support system are your Egun.
Technically Orisa are Egun who have been elevated. We use the catch phrase Orisa but most don't understand that Orisha are many things...not one... But in Yoruba and or the diaspora, the same word is used to describe multiple phenomena. Orisha are people who once lived. They are selected heads because they stood out from the masses when they were human. When they crossed over they were able to perform miracles and became elevated to Orisha. The term Irunmole is what better describes what we call Orisha...especially as it relates to nature. Irunmole are primordials or immortals... These are beings...energies that existed before the earth and universe were formed. When we see the manifestation of Nature, we are witnessing the immortals. Nature has a specific form and function to fulfill to maintain this world. The Orisha are people who were once human. Many times when a person is in possession, they are bringing down a spirit..a person who once lived. That's why you might see a person possess Shango who is from Detroit speak with a Spanish accent in possession even though Shango was a king in Oyo West Africa..who only spoke ancient Yoruba. He has likely brought down ancestor who was a spanish speaking Shango priest.
So when you call an Orisha to you... And set up an altar, that altar becomes a portal between worlds... And you really have no control over what's coming through...or what to do if it starts wreaking havoc cuz you thought you called Ogun but you got Hitler instead..... Or yo Cuzn nems ex con dead boyfriend. There are safeguards that are put in place and specific invocations used to protect initiates from that. There is also a specific formula that is literally placed in the head of a person when they receive and Orisha or Irunmole. They come into existence through specific portals....Odus.. Those portals are marked by the binary frequency they are born in. It is that frequency that is used to plant that Orisha in someone's head or rather awaken that frequency in their head. It can be likened to a phone number in simple terms. You dial the wrong number..you get the wrong thing.. These are why they are mysteries... The universe is mathematical. The odus are mathematical. The whole tradition is rooted in those mathematical odus. When you call Esu there is a specific mathematical frequency that is used... Well technically Esu is all mathematical frequencies.. But you get the idea. While the Orisha names and certain procedures change.. Those portals are still opened with certain keys.
Another aspect of Orisha is what they are inside of you. Going back to the immortals, the wind...Oya...is inside of you as Oxygen.. The breath.. lightening...the electrical system and the mineral copper. Ogun is iron in the blood. These are part of your human nature in nature. And then there is your level of consciousness... Your psychology... .And how that nature shows up in your disposition and character. So if you say you want to work with Orisha, start with the highest character traits of that Orisha and begin to emulate that. That is what being an Orisha devotee is more about. Cultivating character. Be chill and peaceful like Obatala, disciplined like Ogun, harmonious like Osun, adaptable like Oya, or focused like Ochosi. It's not about the right to set up an altar...or worship an Orisha. It's about walking the walk.