I'm not sure what you think nepotism is. Per wikipedia, "Nepotism is the act of granting an advantage, privilege, or position to relatives or close friends in an occupation or field".

The opposite of nepotism is where no one grants an advantage, privilege, or position to relatives or close friends in an occupation or field. That's not "equality of outcomes" by any stretch. A hypothetical system that grants privileges purely on merit would be its true opposite.