No one can really say for sure...I personally believe that they do have genders, but remain sterile for the majority of their lifespans. While males develop into warriors and compete to become alpha male, the females remain as drones save for the queen.
However, the females are all capable of producing facehuggers with resin and a suitable host, but they only do so if they are too few in number. If there are enough drones, the dominant drone undergoes a metamorphosis using the same resin produced to develop eggs but, by not introducing outside hosts, oversaturates its own genetic code and ascends to the level of a queen.
It is also obvious that aliens need to have genders in order to produce eggs without as many mutations. If you recall, in Alien: Resurrection the xenomorphs produced by the queen were still relatively normal. This would not be possible from such a mutated queen unless there were a male xenomorph (aka the alpha xeno) to introduce its own chromosomes and diminish the mutation rate.

"If anything in this life is certain, if history has taught us anything, it is that you can kill anyone." - Michael Corleone