Two complaints: All of the articles I can find are copies of the IJ release. And the title is click-bait.
It appears from the IJ's "details" (https://ij.org/case/nc-engineering-speech/)that Nutt is a chemical engineer. ("Wayne Nutt spent over 37 years as a practicing engineer, mostly working for the DuPont corporation in North Carolina. In that time, he worked with a variety of different technologies and designed and built a variety of things, including pipes for transportation of fluid, while developing deep expertise in chemical engineering and technology.")
He provided expert testimony on a water drainage issue. ("Wayne’s trouble started when he volunteered to testify as an expert witness in a case his son, an attorney, was litigating. The case involved a piping system in a housing development that allegedly caused flooding in nearby areas, and Wayne, who had designed plenty of pipes in his day, volunteered to testify about the volume of fluid that pipe could be expected to carry.")
Then, "After Wayne testified truthfully that he was not (and never had been) a licensed engineer, the lawyers for the defendant threatened to report him to the North Carolina Board of Examiners for Engineers and Surveyors. Wayne didn’t take the threat seriously; he wasn’t designing anything or building anything, he was just offering his opinion about something that might have happened in the past."
Offering expert testimony appears to fall under the definition of "practice of engineering" (https://codes.findlaw.com/nc/chapter-89c-engineering-and-lan...). "The practice of engineering in North Carolina for projects or testimony impacting the public in North Carolina requires that the individual and company must be licensed in North Carolina. ... Our Board considers that any testimony that requires engineering knowledge to adequately provide and to protect the public falls with the definition of the practice of engineering and requires a NC PE license." (https://ij.org/wp-content/uploads/2021/06/NC_Engineering_ema...)
The court appears to have allowed him to provide the expert testimony, but the Board is doing what it does.
There's not much to see here; no one except the IJ is saying anything about "he can't talk about engineering"---the topic in question is expert testimony and I don't think federal courts are going to regard that as some form of protected speech in this situation.