Thus there is no gluon with this color combination. This apparently arbitrary statement is part of the mathematics of color charge. All observed particles are color-neutral objects. They are either leptons , particles with no color charges inside them, or hadrons , particles made of quarks and gluons. Quarks continually emit and absorb gluons.
Color charge is conserved in every such process.
The color-mathematics always works out so that at any instant the entire hadron system is color neutral. When a quark emits a gluon, it can change color. Let us say a red quark becomes a green quark. The gluon it emitted must then carry the colors red and anti-green. The process of gluon emission and absorption occurs only inside hadrons and is not directly observable.