Are there any historical or modern day true stories (like the story of The Buddha) of someone born rich and privileged who just walked away from their family and turned down money and an inheritance?

John Robbins would have inherited Baskin-Robbins (he was the co-founder's son). Grew up quite well off and could have been wealthy through the rest of his life but he chose to walk away from the company due to all the industrialized factory farming and general animal cruelty surrounding the dairy industry. Back then ice cream was all dairy products.

Eventually Baskin-Robbins itself was sold to a multi-national corp & was then sold/acquired a few more times.

https://vegnews.com/the-untold-vegan-story-of-baskin-robbins

https://en.wikipedia.org/wiki/John_Robbins_(author)

IIRC Kropotkin was literal Russian Nobility before becoming ð guy often labeled ð ideological faðer of Anarcho-Communism.

Ð ancoms have been known to call ðis guy "Bread Santa" to give you an idea of what ðis man was like.

So he didn't abondon family, and I don't know that he planned never to return to a life of luxury, and one can certainly criticize American adventurism in the Muslim world, even early 2000s Afghanistan, but Pat Tillman would fit this broader idea, and he paid for it. His parents were a lawyer and a teacher in San Jose, California. He was an unheralded college (American) football player who improved enough in his first few years in the NFL that he went from barely making the pro ranks to being thought of as a valuable contributor who'd have a long and (by any normal human standards) very lucrative career. In early 2002, his team offered him a contract extension worth several million dollars, but he turned it down to enlist as a soldier the US Army after 9/11.

He was known to be outspoken, thoughtful, well-read, and assertively non-religious. While he thought there was a moral case to be made for fighting the Taliban and Al Qaeda, he is reported to have called the Iraq War "fucking illegal." Still, for better or worse he did remain loyal to his commitments and deployed to Iraq. After, he finally went to Afghanistan. He was killed in a friendly fire incident that was covered up at every level, from his platoon-mates burning his uniform, body-armor, and personal journal, to the Pentagon claiming he was killed by enemy fire and coming up with an entire alternative scenario for how he died.

Even once the friendly fire was known, his legacy was being whitewashed to protect the legitimacy of the war and military recruiting, and his family had to fight not to have him remembered as a generic rah-rah "Patriot," but as a complicated man who thought about bigger issues and had a personal moral code not tied to generic notions of 'Murica, Jesus, and Apple Pie.

Does Vivian Wilson count?

Stede Bonnet was a wealthy landowner who walked away from his family to buy a boat and become a really bad Pirate of the Caribbean. Blackbeard ran into him, took his ship, decided for some reason he kinda liked the guy, taught him a few things about piratin’, then went his own way. Bonnet did better after that, but he was eventually captured and hanged.

https://en.wikipedia.org/wiki/Stede_Bonnet

Were you looking for a story of inspiration and success instead of history’s worst midlife crisis? If so, oops.

Jaimie Johnson who filmed the documentary Born Rich (and its sequel) pissed off enough of his family and peers that he was almost thrown out of high society for exposing its underbelly. He also lives a pretty normal life echewing his family fortune which is pretty dope. Might be along the lines of what you're looking for. Good films either way.

ETA check out The One Percent as well, his follow-up from the first film.

Saint Francis of Assisi did this. He renounced his family name, inheritance, and (according to legend) the clothes on his back when his dad took issue with him giving alms. He spent the rest of his life wandering with a small group of other penitents and providing comfort to the sick, especially those with leprosy.

https://en.wikipedia.org/wiki/Francis_of_Assisi?wprov=sfla1

The anarchist Mikhail Bakunin was born into Russian nobility.

Not born wealthy, but there was Ronald Read who lived a modest life resulting in a multimillion dollar estate when he passed in 2014. He left most of it to local library and hospital.

Fredriech Engels and Pyotr Kropotkin both come to mind

Few years ago or so some billionaire said that no one should die a billionaire and donated his money. Or something like that, I don't remember the details clearly. Though I'm not sure it's what you're after as he's done so when really old.