Those little fins are the heat sink for the fan clutch! DON'T shave them off! The fan clutch operates from the heat drawn thru the radiator. As the radiator heats up, the warmed air then heats the fan clutch causing it to "grab" alittle more, thus, drawing more fresh COOL air thru the radiator. This fresh COOL air then cools the coolant. If you shave them fins off, you just ruined the fan clucth.
I installed a 4 core in my CJ5, and my fan clutch did hit my radiator. I looked at moving the radiator forward, but that would have involved removing (unslodering) the tabs. I choose to replace the fan clutch with a flex fan. I now have 3" of clearance.
Now, my CJ was designed for the 2 core radiator. A 3 core might have fit, but it was tight with the 2 core. Not sure what your vehicle is, but if it's a 4 cyl, you can probably get away with removing the fan clutch and installing an electric fan. I wouldn't recommend it for a 6 cyl.
You can replace the fan clucth with a flex fan and still be happy.
As for the minimum clearance betwwen the fan & radiator? As much as you can get! If the front clip comes loose, guess where your radiator is going (if your traveling up a hill clibm for instance) YUP right into the fan!
With a fan clutch, however, the fan can be stopped by the radiator befor it chewes into it. Unlike a flex fan, that spins with the motor! If the radiator falls into a flex fan, It's fan lunch! (till ya shut down the motor)
So, ya got some thinking to do.