I agree, caution still seems justified, whenever we find toxic effects of materials we might contact daily it's worth considering whether the risk that this is a real and present threat is worth the benefits of having those things around. Similar story with Teflon, plastic packaging and utensils, clothing detergents, surface cleaners, micro-beads in face products, cosmetics, talcum powder, deodorant, etc.
For this specific case, I'd still rather see the evidence that most dishwashers, when used according to manufacturer operating instructions (or even when used as most people operate them in practice) actually do leave enough dangerous chemical residue on the dishware to be a risk and that significant amounts of this stuff transfers to food before I'd say it's a claim the manufacturers have a burden of defending. Similar claims could be made about ceramics and glazing for instance, and the ceramics would harm us if ingested, but there's no evidence that ceramics from plates transfer to foods as we eat, even if we cut food on the plate with a knife. Of course, ceramics don't tend to dissolve readily in water either so we can presume detergents and rinse aids have some higher chance of transferring to food if present.
Of course the reality is, if enough people take the sensationalist headlines seriously, the manufacturers will have to defend it anyway; but this effect is what makes organization leaders assume most people are too stupid to hear the truth about nearly anything and the root cause of things like bad nutritional advice recycling over and over again.
Many people are still afraid of stuff like MSG, even though it occurs naturally in many foods and has been proven safe over and over again. The root cause of that scare was a science article in the New England Journal of Medicine back in 1968 which was sensationalized by the New York Times. Bad memes like "Chinese Restaurant Syndrome" are prevalent enough throughout the history of scientific literature to merit an equal portion of caution before reacting to any single paper with too little skepticism or too much drive to change our lifestyles or behaviors.