There are several "conversations" going on already here about printing on fabric. The topic "Washing Muslin Before Printing? " is just one example.
If you want to be able to wash your project, you need to pretreat your fabrice (100% natural fibres only) in a product called Bubble Jet Set. Then - yes - the best results come from printers that use dye based inks. There will be some fading in the first wash, but it should remain colorfast after that. Here's the problem - most printers nowadays are being manufactured to used pigment based inks. Dye based printers are getting harder to find at a price an average person can afford (or afford to save up for). If your printer uses HP Vivera inks, or HP cartridges #10 and 11, you'll get quite a bit of fade in the first wash. You want an "old clunker" that uses HP 78 or 23 (color) and 15 or 45 (black). You have no idea how much I regret having "upgraded" to a photo printer!!! I do a lot of printing on fabric ... or at least I used to. Now I have to postpone a couple of projects I was really looking forward to until I get another dye based printer.
So far, though, I haven't tracked down a new model I can afford. I might have to go hunting for a used one.