Is it possible different coloured quarks have slightly different masses? For example, could the red-down-quark have a slightly different mass to the red-up-quark?
Since quarks rest masses are so much lighter than the particles they make up, that little bit of different mass shouldn't alter their stability. 
Is it possible and how would we tell?
 A: *

*Exact gauge symmetry: If the gauge symmetry (here the $SU(3)$ color) is exact, then the labelings of quarks by colors are just a matter of choices. The exact $SU(3)$ color gauge symmetry should force the quarks of any colors to have the same properties. This includes the same mass, same spin, etc. The colors can be re-labled, and the physics should hold the same.

*Approximate or Emergent gauge symmetry: If one imagine that the gauge symmetry is approximate and emergent as the low energy phenomenon from some high energy (Planck scale or lattice cutoff) systems, then the gauge symmetry may be broken down above certain energy scales $E_{UV}$. The $$E_{UV}$$ can be a higher energy than the deconfined energy scale such as $$E_{dec}\sim\Lambda_{QCD}.$$
Namely,
$$E_{UV} >>E_{dec}\sim \Lambda_{QCD}.$$ 
In this case, even the quark degrees of freedom at this $E_{UV}$ may not even be a good decription. So of course, in that case, the masses for different colored quark may be different -- in fact, the notion of quarks and their masses may not be well-defined.
