Well, I'm in the proccess of figuring out what works for me. The first time I tried it, I didn't have an egg handy, so I tried just vinegar and oil, and a bit of water to dilute it in. It ended up making my hair oily (although it didn't seem dirty). So, then I needed something to wash it with, and I had already thrown out my shampoo. Luckily I had bought a bar of castile soap. It was a brand called Fruits & Passion. I looked at the ingredients and it seemed safe. I washed my hair with that, and that left it soft, and not too oily, but not stripped dry.
Today I tried the recipe, with the vinegar, oil, and egg. That also ended up making my hair oily, although it is clean. I think I will try what my friend does. She puts coconut oil in her hair for two hours before shampooing. Maybe I should put coconut oil in my hair first, and then wash it out with a mixture of 1tbs vinegar and 1 egg.