While it is safe to apply texturizer to relaxed hair, it is not recommended. Texturizer can be used on new growth, but very careful application is required to avoid causing damage to the already-relaxed hair.
Relaxers and texturizers use a lot of the same chemicals to straighten the hair or soften curls. Texturizing formulas are milder than relaxers and are meant to be applied for shorter periods of time. Because of this, people don't always realize that texturizing relaxed hair is very much like relaxing the hair twice, which can cause severe damage. Blow-drying, wet-setting, and flat-ironing relaxed hair are safer ways of achieving the desired hair texture.