There are plenty of people in current government who are de facto not accountable to the public. Sometimes that lack of accountability is even intended by design. Are Supreme Court Justices accountable to the public for their interpretation of the law?

I said semblance of accountability for a reason. Still, Supreme Court justices are appointed in limited number by elected politicians - who have to justify the appointment based on their supposed professional credentials - to discharge a specific set of duties

They certainly would not be more accountable if their appointments were more aristocratic in character (i.e. they inherited them from their ancestors who had been appointed for arbitrary reasons by an unelected monarch) and, like aristocrats, they didn't have to explain how and why they exercised the powers given to them.

On paper, SCotUS _can_ be held accountable by the public through their representatives. The process is called impeachment. The house _can_ impeach a sitting Justice, and the Senate _can_ vote to remove them from office. This currently is unlikely, but the it _is_ possible.

The "easier" route is for the legislature to "see" the ruling and pass a law that counter-acts it. The general public can _also_ call their own Constitutional conventions and pass amendments to the Constitution to hold SCotUS responsible.

The real "problem" is all of these solutions, by design, require significant effort. If you want changes, you will need to make them happen.

They can be impeached. So I think if their interpretation was wildly wildly wrong, they could be impeached.

But impeach a majority of them? Impossible in reality.

I’d be shocked if even one is.

A political mechanism defined on paper does not mean anyone will ever invoke it.