I believe infant intersexuals should be assigned a specific gender at birth because the paperwork calls for the information and it is pretty much impossible to process without a designation. What is on a piece of paper shouldn't be troubling to people, after all, it is just a document. This shouldn't change how the individual is raised, nor be the guide to an answer for them. They are truly unique and their parents should explain that to them.
At first, I would have said, yes, pick what the child is, but in today's world I believe that parents should wait. A substantial matter of time should be given in order to see what characteristics surface within the child. I also think that it would depend on the organs present that are actually functional.
No, infant intersexuals should not be assigned a specific gender at birth, because that would be making an arbitrary determination. If a child is truly intersexual, they should be listed that way. That way there is no confusion later on. If later on they want to change that, then go ahead and change it.
Intersex babies should most definitely not be assigned a gender at birth. These individuals will have to go through enough persecution and misunderstanding throughout their life as it is. They should be free to discover their own identies naturally as they come into maturity. It would be unfair to artificially decide this for them in advance.