But the fact that he is not selling the furniture should.
According to the article, someone has complained that he is "producing odors and noxious fumes," basically the same complaints someone might make if the next door neighbor smokes. Unless he is running a large scale operation, some drying varnish is not going to reasonably affect any neighbors.
If he is not running a commercial business and the "odors and noxious fumes" do not rise to the level that someone could successfully sue him as a public nuisance (generally pig farms and waste dumps) then it is his business what he does in his own home.
Of course, that is why I refuse to live in a subdivision with a homeowners association or in a house within pissing distance of a neighbor.
As to the odors and noxious fumes.... I assume the HOA is also clamping down on anyone who dares to paint or re-stain their decks or fences. Also some yard service treatments emit odors that might be offensive to some sensitivities.
I manage a HOA with 1900 homes. This would be called a home occupation and the complainant would be told that nothing could be done to stop someone from enjoying their home occupation. What happens when he has to paint his house? The yard furniture? The fence? Sounds like he has an angry neighbor close by to me.