Actually, this is one I haven't read up on yet. I'll see what I can do!
I suspect "toxic" is a strong word to use in this case. Personally I would use it as the dictionary originally defined it -- poisonous, causing injury or death by chemical means. Some inhaled products are genuinely toxic. PTFE fumes are a case of that. Paint thinner is probably also a case in point. Others have an irritant effect, which is not desirable and may make the bird temporarily more vulnerable to disease, which I think is the case with most household fragrances. That's undesirable, but not an immediate emergency. But I don't know about dryer sheets -- I'd actually be more concerned about the component that is anti-static more than the scent itself, but as I said I haven't looked into this carefully.
I use "free and clear" detergent most of the time anyway, because some of the scented ones make me itchy. I do use dryer sheets, and I've had my birds do as ReaRea does and help with the laundry without noticing any adverse effects, but I don't use scented products when I'm washing anything that's going into the cage, like the rope perches.
I'm going to guess this is one of those things where it is totally unclear, and if there is a problem it may be brand dependent. I've heard people suggest using dryer sheets to clean cages as well as hearing that they are a no-no.
Personally I'd probably avoid using strongly scented laundry products on anything that would be in close proximity to the birds for long periods of time, but I don't really worry about my clothes or towels or bedding...
I'll see if I can find anything out that has solid basis.