There is nothing wrong with having family ties to Nazis. You can’t choose your family.

There is everything wrong with doing Nazi things, regardless of who you are related to.

Quick search surfaces a couple articles, both paywalled.

From The Atlantic: Elon Musk’s Anti-Semitic, Apartheid-Loving Grandfather

From The New Yorker: The World According to Elon Musk’s Grandfather

A quick skim of both basically points to how his grandfather was a racist actively involved with fascistic, anti-semitic political organizations and publications. Quote from The New Yorker article below:

In the nineteen-thirties, he joined the quasi-fascistic Technocracy movement, whose proponents believed that scientists and engineers, rather than the people, should rule. He became a leader of the movement in Canada, and, when it was briefly outlawed, he was jailed, after which he became the national chairman of what was then a notoriously antisemitic party called Social Credit. In the nineteen-forties, he ran for office under its banner, and lost. In 1950, two years after South Africa instituted apartheid, he moved his family to Pretoria, where he became an impassioned defender of the regime.

However they also both note that Musk’s grandfather died when he was two or three years old, and The Atlantic article notes that Musk’s father didn’t seem to follow too closely in his father’s footsteps. Quote from The Atlantic article with original links included below:

And Haldeman’s politics were not universal in the family; Elon’s father, Errol Musk, for example, was a member of the Progressive Federal Party, the primary political parliamentary opposition to apartheid.

You could try asking LLMs. The ones that don’t actively search the web for answers are capped with knowledge up to when they were trained and won’t know about it. But verify whatever they tell you in case they make it up.