Go to Options -> Controls and set Gears to Manual. You also have the option to select whether to use a clutch or not at that menu as well.

I created a cheat to do this using the cheat engine.

TL;DR
For shift1 replace memory at 004BDE30 with ret 0008
For shift2 replace memory at 00551550 with ret 0008

WARNING! This is a hack. If you do not follow these instructions exactly it could corrupt your save game OR WORSE! It may break something even if you do follow them to the letter. Use at your own risk.

Now with the big scary warning out of the way. This hack seems pretty stable and the worst that I've experienced is that the game crashes. In that case I just rebooted the game and everything was fine.

This hack only works for the steam versions of nfs shift 1 and shift 2 unleashed. The procedure for applying this hack for either game goes something like this.

1. Launch either game and then open the cheat engine.
2. In cheat engine click on 'select a process to open' (the computer icon in the top left under File) -> Select the game executable in the Applications tab -> Open -> click on Memory View -> right click on any address in the memory viewer -> click 'Go to address' in the menu that pops up -> for shift1 type in 004BDE30 for shift2 type in 00551550 -> ok.
3. Now you should see the Opcode 'push ebp' highlighted (this will be the same for both shift1 and shift2). If you do not see this then don't proceed or else you might break something e.g. corrupt your game save.
4. Right click on that Opcode -> click assemble -> for either game type in ret 0008
5. To undo the hack just reboot the game.

Now you should be able to drive backwards in the shift games. Have fun with the carnage :D

How does this hack work?

This hack disables a function from being able to run and I think this function checks to see if you're driving backwards, and has some logic to determine if it should disqualify you. If it never runs you can't be disqualified for driving backwards. You can still get disqualified if you cut too many corners though.