Friction both supports and opposes every one of those sports.
For running, you need friction under the sole of your foot. On the other hand, the friction of the molecules in the air moving past your body is providing resistance.
For car racing, friction is needed under the tires for that car to go zoom. But friction also opposes the car with the drag of air molecules.
Same principal for horse racing. Friction is needed under the shoe of the horse, while it opposes the direction it's running via drag resistance.