The stereotypical brown dwarf will react with indignation if you point out that it is not truly a star. It will puff up at you, its banded complexion evening out just that little bit. Many may point out that, despite their power source being their own contraction, they once experienced the heights of deuterium (and, perhaps, lithium) fusion. Careful not to find yourself on the back foot if they bring up their cousins the white dwarfs- once someone's seeded the idea that they're a living manifestation of the death that most stars are headed for, you may find it difficult to keep being rude to them.
Of course, nearly all brown dwarfs simply will not care. There are plenty of brown dwarfs who occupy planet-like positions in their respective systems, some even without worlds circling them- they may well be confused that that's even a question. Claims of being an especially heavy gas giant should probably be rebuffed, though....
Farther out companions or singlet brown dwarfs will often likewise agree that it does not matter, though usually on a moon-focused side. After all, even gas giants can impart large amounts of heat to their moons without other stars to light them. If your nearest world reaches heights sufficient to melt water with your help, would you care that you're technically not a star?
Brown dwarfs love hard. If you attempt to bring this up to bonded pairs of brown dwarfs, their rebuff will be strong. In fact, they may well add up in many ways to match a small red dwarf. Some are so closely tied that they may claim they are a red dwarf together, though very few finally go in for the kiss- er, collision.
The most annoyed reactions will probably come from high-temperature brown dwarfs (and pre-ignition red dwarfs). After all, they burn hot enough to match some giants! Some of the brightest may well lack any clouds, a feat that even some red dwarfs are hard-pressed to match. Though they may well cool off on spans low-mass red dwarfs would find laughable, for now they may shine bright enough that a nearby civilization without telescopes might assign them a name- truly a grand feat.
