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Yesterday I was playing in multiplayer. After finishing I get Back to lobby and changed my car, but by that time I was a bit late and a host already changed the track. In a Waiting room I've pressed Tab to join, connected before the race started and was able to race, but the car didn't change.
Once the host changes track, your car and your position in the grid for that race is fixed. Any changes to your car afterwards only take effect for the next race. I'm marking this topic as invalid (not-a-bug).