For the clarifying wash yes you need a shampoo with sulfates in it.
Conditioners don't contain sulfates, that's a cleansing agent and conditioners don't clean your hair.
It's silicones you need to avoid, otherwise you'll need to use a shampoo with sulfates in again to get the silicones out.
Shampoo that doesn't have sulfates in it isn't really shampoo. The CG community refers to it as low-poo because it does contain other cleansing agents. Maui is low-poo, I know because I use it.
With cowashing (literally means conditioner-only washing) it's the action of rubbing your hair/scalp that supposedly cleans it, not the ingredients in the conditioner.
Maui make conditioners too, if you're going down the cowashing route, or if you want to follow your regular low-poo/clarifying sulfate shampoo with a conditioner. I don't know what ingredients are in the conditioners, I've never looked,
I do know that it's not uncommon for a conditioner sold as suitable for curly hair to contain silicones, when the matching low-poo to go with it doesn't contain the sulfates that will get the silicones out - AKA a recipe for disaster. Or the shampoo does contain sulfates but also contains silicones itself. "Suitable for curly hair" is a subjective phrase.
AFAIK everything by John Frieda is packed full of silicones (as are a lot of products marketed for curly hair) including their shampoos! It's years since I've looked though so my knowledge could be out of date.
Any words ending "cone", "conal", "xane" is a silicone but there's others. If you're solely cowashing or low-poo, you'll have to become an expert on ingredients that are silicones. And check your products regularly because companies have a habit of bringing out "new and improved" formulas that aren't, without telling customers. So you find out when your hair inexplicably goes to shit and you get round to checking ingredients. You'll have to check ingredients on styling products too, not just shampoo and conditioner.
Silicone is coating your hair in plastic. Favoured because it makes hair easier to detangle. If you don't remove them these layers build up, meaning no conditioning agents can penetrate the hair shaft and your hair will get drier and more frizzy and develop split ends and become such s PITA to brush that you go looking for a detangler spray/serum/whatever product (which is pretty much guaranteed to contain silicones). Breaking the vicious circle (and keeping it that way) means avoiding silicones first and foremost.