1) That a lot of allergic reactions come from actually touching a dog or having the dog touch something; they don't need to leave fur behind for that to happen.

2) That licking hair/fur releases the same amount of dander, whether your shedding fur, hair, or neither. Matter is conserved.

3) That clumps of fur are easy to avoid.

Those are fair points, but I’m not convinced that fur doesn’t have an impact.

Anecdotally, I have a mild cat allergy and own a cat. Vacuuming our sofa regularly makes a huge difference, as it gets rid of the fur stuck to it. It goes from feeling scratchy to totally fine.

Maybe clumps of fur are common with super fluffy pets? Ours is a shorthair and shedding leaves single hairs lying around.

Matter is conserved, sure, but fur with dander stuck to it from saliva versus skin with saliva on it, surely makes a difference?

I'm less concerned about fur with dander stuck to it then simply furniture with dander stuck to it.

Three things to consider:

1) You can't see dander.

2) Vacuuming helps with pollens, and with dander from animals without fur too.

3) You have mild allergies. Others have stronger ones. I have no scientific basis for this, but I suspect sometimes, the immune system goes into maximum overdrive.