What about babies born at the same time and place?  Doesn't astrology anticipate that they should be almost identical even though they have different parents?

Actually, we would expect very similar characteristics in these "astro-twins" or "time-twins".  Despite obvious differences of genetically related characteristics such as skin, hair, and eye color we would anticipate comparable potential for these "astro-twins" as suggested by their identical birth charts.  

Divergence arises because of the environmental differences (especially financial and educational) and the expression of free will and decision-making that will form variations in results with the non-biologic "twin".

I find this question quite fascinating, since it emphasizes the importance of not being predestined to a specific outcome.  Astrological probabilities suggested by our birth chart corresponds to our potential.  Although these individuals may begin with identical potential, it is not very likely that they will continue to live mirror-image lives (although some "Believe-it-or-Not" type cases are quite amazing, for example identical twins being separated at birth and living parallel, almost identical lives — though this isn't really what we're discussing here).  

Even sharing the same basic strengths, talents, and challenges astrology  allows substantially different outcomes or manifestations — while still remaining within the suggested range of astrological expectations.