I beg to differ. I do it all the time. What’s more, I do it with non-toxic materials. Check out this 100% polyester polo shirt tie-dye. Sorry it’s such a bad photo, but the only camera I have right now is my phone.
Since I’ve told dozens of people IRL about this, and since no one ever bothers to use them besides me, I’ll share my secret with any Doper who reads this thread. I’ve been using these products to tie-dye for over 25 years now.
The iridescent ones are tricky to use, and the transparent ones don’t work well at all, but all of the opaques and fluorescents work equally well on cotton, silk or polyester. They are water-based, so diluting them is easy.
I’ve used them to dye a few items “whole cloth”, and that is kind of tricky because you have to make sure that the dye gets applied evenly and stays that way as the item dries. I usually dilute in a bucket, let it soak for a day or so, then dry it flat. If there are still anomalies, I repeat the process. Black is still difficult, but can be achieved by diluting as little as possible.
Once the article is dry, you just have to iron it to get the dye to set.
These colors will never fade once they are set into the fabric, btw.
Now that said, these aren’t cheap. You can find them at some fabric/hobby stores and prolly at a real art supply store, or you can order them online. I get mine from Dick Blick Art Supplies.
For tie-dying, the small 2oz bottles will do colors for 4 or 5 shirts, as long as you dilute them a bit with water. You really have to do this, so the color will spread thru the fabric and not just blot up where you apply it.
For whole cloth dying, I get the 16oz bottle. I use roughly half at once and dilute it as little as possible while still being able to completely submerge the article of clothing.
Again, whole cloth dying is hard because it’s difficult to achieve a flat, uniform color with this media. I keep meaning to get a sprayer and try that, but so far I’ve not bothered; I wear a lot of tie-dyes. 
But, if you want to do some creative dying, and want to use easy, non-messy (cleans up with soap and water), non-toxic media that will produce vivid non-fading colors, this is the way to go IMO.
If anyone wants, I can post pics of other shirts (cotton & poly), silk scarves, etc.