Color charge is always conserved.

When a quark emits or absorbs a gluon, that quark's color must change in order to conserve color charge. For example, suppose a red quark changes into a blue quark and emits a red/antiblue gluon (the image below illustrates antiblue as yellow). The net color is still red.

Quarks emit and absorb gluons very frequently within a hadron, so there is no way to observe the color of an individual quark. Within a hadron, though, the color of the two quarks exchanging a gluon will change in a way that keeps the bound system in a color-neutral state.