I have heard that males and females specialize in different stats, but I have forgotten which ones. If I have a male Spinda and a female Spinda, with otherwise identical properties (Nature, EVs, and IVs), will they end up with different stats at level 100, solely because of the difference in genders?
No it does not affect stats. In Generation II, the gender was based on the attack IV, but not anymore. Gender does affect other traits which are also listed in the source I have listed. Things like what is passed on to the egg as well as moves like Attract.
Gender makes no difference in the stats of a Pokémon after Generation II, unless the two Pokémon are a different species entirely, such as Nidoran.