As expected, the judge relented:

http://www.nydailynews.com/ny_local/..._by_judge.html

The judge affirmatively stated that he imposed a sanction because of his view that the juror was seeking to avoid jury duty:

On Wednesday, he made it clear it wasn't her views that angered him but what he said was her obvious attempt to weasel out of jury duty by lying.

"My ruling was not based in any way upon whether or not you held any racist views. It was apparent you did not tell the truth," Garaufis told the woman.

"You were the only juror who indicated that you had every form of bias imaginable. You were lying to the court in order to be excused."
The story also makes clear that he was concerned about encouraging others to take that approach in an effort to avoid jury duty:

"The purpose of this order was to attempt to create some consequences or disincentive for people who intentionally obstruct the court's ability to empanel a fair and impartial jury," he said.
No matter his reasons, several experts agreed that his order likely violated the First Amendment:

NYU Law Prof. Stephen Gillers said the judge had no choice but to find her in contempt for lying, or release her. Obnoxious opinions, he said, are not criminal.

"She can't be punished for being a racist," Gillers said. "You don't check the First Amendment at the courtroom door."
The woman seems to have reprehensible moral beliefs. This is America, and she’s en led to possess those beliefs. But government officials are not en led to punish people for those beliefs, including by requiring them to serve more jury duty as a result of their beliefs.
Eugene Volokh