This idea/topic has been brought up and discussed across many forums and breeders. From my personal husbandry experience and reading discussions (similar to what happy1892 posted) it is predominantly environmental. While genetics may play a role, the environment plays a bigger role.
However when you ask "...can change color..." it is understood that a mantis can't really change color (like the immediate color change in chameleons or Cephalopods). However, usually the only time a mantis changes color is gradually over time (over several molts) but in some species a few days after their latest molt, which is most predominant after their final molt, like in orchid mantids, Hymenopus coronatus or giant devil's flower mantids, Idolomantis diabolica the color change can seem more immediate.
In summation, yes it is possible for some species' of mantids to change color based on their environmental conditions/surroundings.
Cheers,
Andrew