I have just recently bought the game and noticed that when in arcade gearbox mode in any vehicle, it stays in reverse. note: I do not have any mods, the game is vanilla. I was hoping there is a current fix to this or the devs will see this and look into it if more people have this issue.
Do you hit brake to stop? In (arcade) reverse than it is the gas. Use the forwards arrow to brake in reverse and start moving forwards again.
your brake pedal is probably stuck on, maybe even at 1%. Open pedals app in the UI and see (or check brake lights ) If it is then extend the deadzone of the pedal using either the software or BeamNG.drive