Will my Race fuel consumption be different than during normal cross-country flights? How much different?

This is an “it depends” answer. The competitive spirit emerges in a big way when the starting flag drops.
Airplanes flying the Air Race Classic must be rated for continuous maximum power – for a reason. Winning depends on maximum power. Maximum power gobbles fuel. The altitude and temperature have some impact on how much. Practicing this kind of flying is a good idea. To be safe, expect your airplane to use as much as 50% more fuel while racing. This is another area where your Mother Bird can offer advice.