The coconut oil is key for the texture of this cheese. As you might know, coconut oil has a high melting point compared to other oils (that's why it's solid at room temperature instead of liquid, like other oils). So when you refrigerate the cheese mixture, the coconut oil helps solidify it, leaving you with that sliceable texture. If you are strictly oil-free, try my other oil-free cheese options (Vegan Queso and Nut-Free Cheese Sauce). If you are allergic to coconut products, you can try using olive oil, but I don't know if you'll get the same sliceable texture, as coconut oil is solid at room temperature.