From Easton:

No grease on carbon posts. Grease contains certain minerals that can attack clear coats, can penetrate the resin matrix and could cause swelling of the composite laminate. Can you say "stuck seat post?" Don't use grease.
John G. Harrington
Vice president, bicycle products
Easton Sports, Inc.

From Campagnolo:

No grease. In some cases it can be dangerous to use grease as the chemical composition can cause a reaction between materials. Besides, it increases the torque required to clamp the post.
Richard Storino
Campagnolo USA

From Deda:

Absolutely no grease on carbon, ever. Also, do not use solvents to get old grease off, or to get old grease out of the seat tube. John Harrington of Easton and I believe that many solvent residues in the seat tube soften the gel coat of the carbon, then bond the gel coat to the inside of the seat tube, freezing the seat post in position for eternity.
Tom Franges
Deda Elementi North America tech support

From Bontrager:

There are some petroleum greases that are slightly acidic. That acidity can attack the resin used in carbon-fiber construction (frames or posts). This same acidity can attack aluminum or steel frames components, too. However, most greases are engineered to be slightly basic. Neither Trek's nor Bontrager's carbon resin is affected by this acidity. The main reason we suggest you don't use grease on any seatpost inserted into a Trek OCLV frame is that there is not enough surface roughness inside the seat tube to ensure your post stays where you put it.
Scott Daubert
Trek team liaison