|In theory ME doesn't recomend the use of whitening agents such as Oxy-Clean. Many diaper manufacturers do recomend it though and it is a fairly common additive in the cloth 'world'.
Also this recipe contains no surfactants at all. Washing soda is a water softener and helps by making the water more alkaline (washing happens better in alkaline water). Borax and Oxy-clean are both disinfectants and whiteners and oxy-clean also turns partly into washing soda once in water.
They're all useful ingredients and all relatively safe (the Oxy-clean may be a bit controversial but it's not likely to 'ruin' your diapers or anything like that, just if you're washing more sensitive fabric like bamboo perhaps take note). But the recipe is missing a surfactant as I said. Surfactants are a fairly important component of a detergent. They break the surface tension of the water and allow the water to 'clean' away the dirt and bacteria.
Now..... all that said... This is a popular recipe for washing cloth diapers and many swear by it. I did want to kinda cover the more official scientific stuff but all that doesn't mean that it can't work. And there's no reason why it would be any less safe or effective with ME diapers. And if you really want to stick with more natural and inexpensive stuff you could always add a couple soap nuts since the saponin they release is actually a very good surfactant. Not to mention completly natural, safe, clean rinsing and eco-friendly.