Yes. Naziism is terrorism. People lose their jobs for publicly supporting terrorism. The employee was self-proclaimed "Nazi" (including to quote, "I'm a nazi", posted publicly while working there) per views and advocacy. They also took over leadership of "GNAA" from Weev (a Nazi with Nazi tattoos etc.) while employed at Cloudflare (I won't type out what it stands for here)
Even Wikipedia does not describe that organization (I assume you don't mean the Greater Nashville Apartment Association...) as itself an extremist organization. (It is also described as defunct.) By its very nature, statements by its members (which you have not evidenced) cannot be taken at face value. Auernheimer's views are his own. The only identification I can find of a possibly other leader of the organization (who you have not named) leads to nothing that confirms any detail of your story - not the supposed Nazism of that person (assuming it's the right person), nor employment at Cloudflare, nor any knowledge on their part.
In short, I can find no good reason to believe this.
