You don’t know that much about the movies of the Matrix.
Neo isn’t white. He passes for white but Keanu isn’t white.
But even if he was white, the idea of the One is way more complex than a “saviour”. The “white man computer program” (I assume you mean the Architect) created the One in the first place as a means of control, to try and manipulate anomalies within the Matrix and keep them all within control. So being the “One” is not a good thing actually.
The Oracle is also not controlled by the Architect. At times she works with him, at other times she works against him.
If you say the Oracle is a “ghost in the machine”, so is the Architect (the “white man computer program”). Really neither the Oracle nor the Architect are human, their appearance is whatever they want it to be, so they chose those appearances for a reason, perhaps because they thought that it would influence people easier to trust a friendly motherly looking Black woman, and to fear an old autocratic looking white man.
The thing about both the Oracle and Morpheus, is that they USE Neo for their own ends. He’s like a weapon for them. That’s not the same as a “magical Negro” or “white saviour” trope, if the supposed “white saviour” actually is being manipulated to serve the larger goals of the Black characters.
The Oracle’s overall goals is to create peace between the humans and AI — this is explained further in the Animatrix where you see that it was the humans’ fault the war started and the world was destroyed, because they couldn’t accept AI having consciousness or deserving rights. And the reason that the Matrix was initially created was as an alternative to genociding the entire human race. The AIs couldn’t trust that free humans wouldn’t try to wipe out all AI if they were allowed to be free. So they decided to imprison them instead, and because humans took away the solar energy the AIs used for power, the AIs decided to use them for energy instead. But they tried to create a heavenly world for humans, where they would never suffer, and only because the mind rejected that did they create the more imperfect Matrix.
The Oracle wanted a world where humans and AI could both be free and yet have peace. That was her long term goal and she had seen 6 iterations of the One fail in this test, since the One was used by the Architect to maintain the integrity of the Matrix instead. Finally Neo broke that pattern and overall the Oracle’s aims were achieved — peace between free humans and AI.
Not all AI or humans wanted peace — but many did, and in Matrix Resurrections you see the creation of Io, a blended city where free humans and AI can work together in harmony and friendship.
But Morpheus’s goals were different from the Oracle’s. He wanted peace yes, but he thought the only way to have peace was to destroy the Matrix.
Even after The Matrix Revolutions, after Neo had helped broker peace between humans and AI, Morpheus in The Matrix Online attempts to destroy the Matrix — bombing it and killing many blue pilled people still in the Matrix, which ended up causing a war between the old Zion and the Machines. This led to Zion being destroyed and Morpheus was killed.
So you can see that while both the Oracle and Morpheus do really care about The One, they both want to use the One for their own aims, which are not the same. The Oracle wants lasting peace between the Machines and humans. This means not destroying the Matrix but freeing people from it, so long as they want to leave. Morpheus wants peace he’s willing to do so by destroying the Matrix. The Architect wants “peace” by maintaining the Matrix and keeping as much humanity inside it due to the fear that free humans would cause war. The Analyst wants to use Neo for this purpose also.
The commonality is that instead of Neo driving the story, Neo is actually not the one in control most of the time. His choices are very rarely as empowered as he believes them to be at the time. That’s one of the interesting things about the Matrix movies. Just because Neo is the main character doesn’t mean he is actually the one controlling events the most.
It reminds me of the Hunger Games series. Katniss is the main character, but she is NOT the saviour. She is a figure head, manipulated by competing interests, who all try to use her as the Mockingjay or as a tool for Panem propaganda. She does have some agency, but it’s not that everyone follows her and she comes up with all the ideas.