Found this bug with the windshield wipers. If you activate them (with R3) and restart the race, they will still be enabled. This occurs with all tracks and all cars. Is this a mistake or something? Please tell me.
The wiper's state is probably not reset upon restarting since there isn't any big loading zone. It's not a game-breaking, hence the low priority/unwillingness to fix it.
I haven't experienced anything like what you're describing, but I noticed something something odd with wipers when doing the Suzuka race a few months ago. I couldn't shut the wipers off, even after the rain stopped. I thought it might be my controller, but eventually as the track dried, the wipers shut off by themselves.
When simply "restarting" the same race "that you are currently in" the wipers staying on is normal. Simply turn them off. The wipers also will stay on when the rain stops provided the road is still wet flinging a water trail. When the road becomes dry I believe they turn off automatically in a race if I recall correctly.