Carbon-carbon (CC) grids were used on the mu10 microwave discharge ion thrusters on the 'Hayabusa' asteroid sample return mission. They are being used at this very moment on the Hayabusa2 spacecraft. I believe CC grids are planned to be used on the NEXIS engine for the NASA Jupiter mission and the Cross Enterprise Technology Development Program (CETDP).
CC grids are superior to molybdenum grids in terms of thermal expansion (CTE of CC can be made virtually zero, CTE of Moly is about 4-5*10-6 /K) and sputter yields (2.2 at 45 deg for Moly compared to 0.5 at 45 deg for CC @1 keV). These are very important criteria for long-duration missions. However, fabrication of CC grids is lengthy, complex and expensive, especially when you want dished grids for improved structural rigidity (grids are typically domed/dished in thrusters over 15 cm in diameter). Molybdenum grids can be chemically etched with very high accuracy much quicker and for a lot less money.
Also, molybdenum grids have higher strength (655 MPa) and elastic modulus (324 GPa) so they can be made thinner and more transparent (i.e. with higher open area fraction) than CC grids (strength=345 MPa, E. modulus=206GPa). For a given grid diameter, the thickness and open area fraction suitable for Moly would make the CC grid too fragile and prone to warping after machining/drilling. Reduced screen grid thickness with higher open area fraction means that Moly grids have better electric field penetration into the plasma and can extract greater ion beam currents (i.e. higher ion transparency) than CC grids.
So while CC is a very good choice of material for ion optics, it is very challenging and expensive to machine to the desired geometry. The thinnest CC grid I've heard of had a thickness of 0.46 mm . Its flexural modulus was highly anisotropic and it had to be laser drilled (mechanical drilling was too difficult), which caused tapered holes. On the other hand, Moly grids can be comfortably made 0.25 mm thick .
Hope this helps.
 Mueller, J., Brophy, J. R., and Brown, D. K., “Design,
Fabrication and Testing of 30-cm Dia. Dished CarbonCarbon Ion Engine Grids”, AIAA96-3204, 1996.
 Development of an High Performance RFIon Thruster; R. Killinger, H. Bassner, J. Müller, DaimlerChrysler Aerospace, Munich, AIAA-1999-2445