We know it's accurate because they brag about it [1]. This isn't hard.
[1] https://www.vice.com/en/article/93wnja/neo-nazis-boast-about...
You're assuming guilt by association, and probably falling to Godwin's law. There's a difference between what someone may be, and what you may say in the workplace. The fact that the person who said is is Jewish means nothing, it's only a distraction from that an employee referred to a group of people as Nazi's and the employer took a offense and..the employee is looking for a new job.
You can't fire someone for behavior and excuse it in the other simply because you agree with their politics.
> "A coworker was quick to criticize the employee for using divisive rhetoric, igniting a firestorm of internal debate, with many jumping in to take sides. That same day, HR reprimanded the employee, who is Jewish, for using the word "Nazi" in the workplace."
The disruption in the workplace is probably enough to get HRs attention.
Now to answer your hypothetical question, I think the word Nazi has deeper connotations than the use of "gangster", but in either case I don't think the words should lead to termination. To quote a man I do not like at all, 'We have a snowflake generation', Dan Pena.
It’s not “assuming guilt by association”, it’s pattern recognition.