Brave New Work doesn't assume genetic determinism at all. All the manipulations to produce the different castes are environmental, either prenatal (exposing the fetus to radiation, chemicals, etc.) or as the result of behavioral conditioning.
You're right, though; I just went back and re-read the first chapter, there's no mention of the different castes being differentiated until after fertilization. Of course there's much we know now that Huxley didn't know about genetics, so if you were to try to start up a Brave New World society then genetics would be the right place to start.
Other technological problems with BNW include the attempts to teach values by subliminal messages during sleep, which afaik have now been pretty much proven to be a bunch of hooey.
The main problem, I think, is that you'd almost certainly always wind up with an overlap between your castes -- your smartest gammas would be smarter than your dumbest betas. That's not necessarily a big problem, though.