Not at all, you're presuming there are many different ways life could work, that might not be the case at all. It's entirely possible there's only one or very few possible recipes for life so no matter how many abiogenesis events occur, they produce the same kind of life.

A simple analogy, wood burns, fire is fire, you don't expect every different occurrence of fire in nature to produce a new and incompatible type of fire. Life could be the same, it could be that anywhere carbon based life forms it's basically the same basic recipe and thus biologically compatible with all other forms of carbon based life.