A cadaver may contain human material which might spread disease, but not the cremated remains of a cadaver.
Yes you could say the ashes that remain were once human material, but ashes are primarily made up of the material bone is composed of (tri calcium phosphate). Tri calcium phosphate is put in salt and also added to toothpaste.
Bodies are cremated at temperatures exceeding 1600 degrees F. This reduces the body to basic chemical compounds and certainly kills off anything that might cause disease. Ashes are non-toxic and safe. (although you might not want to ingest them in concentrated amounts as they may contain heavy metals.
Sorry, but it is totally irrational to remotely suggest that the ashes that remain from cremation are capable of spreading disease.
I believe those that oppose coming in contact with ashes have some basic phobia about dead people and dead humans in particular.
I ask those who are afraid of touching, ingesting, or inhaling the basic chemical compounds that once were part of a human body: Do you eat meat? Doesn't it freak you out to put the visible remains of an animal in your mouth and swallow it?
The chances of catching some disease from eating meat are a million times greater than any problems you might have with ashes that remain from cremation.
Everyone has eaten some plant or animal that has contained at least some basic chemical compound which was once part of human body, and you will consume many more of these in the future. You have basic compounds inside you right now that were once part of some dead person.
You have inhaled and swallowed skin cells that have sloughed off other people.
You have inhaled carbon dioxide which was exhaled by someone else, and the carbon was once part of a sugar or fat stored in their body.
Think about it.