I think no-poo is safe for dyed hair as far as I can tell/have heard. In fact, I've heard it makes your color last longer.
Just an FYI, though, doing baking soda a lot can damage your hair... I don't cut my hair that often but the first cut (6 months or so?) after starting no-poo with liberal baking soda, I had horrible splits. here's what I learned... baking soda has a pH of 8, vinegar has a pH of 3 or so, and hair normally has a pH of 4 or 5. Water, pure water, has a pH of 7 (but that can vary depending on what's in your tap water). Ideally you want your hair "pH balanced"... so you just gotta watch what you're doing. I find that if I feel like my hair needs to be washed but instead I jump in the shower and scrub/massage my scalp (scalp, not hair!) with just plain old hot-ish shower water, for a while... like think minutes, not seconds... it makes a huge difference in the greasiness and doesn't kill my hair like the baking soda does. I rinse with a teeny bit of vinegar in a full bottle of water to try and restore the pH. I'll do the baking soda if I'm desperate, or I guess like maybe once a month? It does take time to work up to doing less and less and let your hair get used to how much oil it's supposed to have, but honestly you can get a sulphate free shampoo (which doesn't strip your hair as much as regular sls or what-have-you shampoo) and work your way to less and less often.... also use less shampoo... like a teeny drop.
I've been no-pooing for more than a year and a half and that's what I've found works best for me (well, I do'nt shampoo, ever, but that's what they recommend to get away from stripping the oils as much, if not baking soda)... but like I said, just be careful with the baking soda
I'm sure not everyone will agree with me, though, so if it works for you, awesome
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ETA... just something else to consider... hard water makes no-pooing harder. If you have very hard water, check into no-poo suggestions regarding that. I stayed at a place on vacation with EXTREMELY hard water, and by day 4 my normal no-poo routine was NOT acceptable and my hair felt sort of nasty and waxy. Ew. Anyway, there's lots of resources out there talking about what to do with hard water. Also, there's a livejournal no-poo group that has a lot of good no-poo troubleshooting advice
