I bought all new parts for the entire brake system. I got this brake booster but it compresses the piston of the MC pretty hard to put it on. Do I need to remove this metal insert or is this part not compatible?

 

No do not remove the retaining clip. The push rod on the brake booster is adjustable, also when installing the MC there will be a small gap that will lose when fully seated.
Best thing to do is if you have the original parts off the car, measure the depth of the cylinder inside the MC and also measure how much the rod is protruding out all in comparison to the replacement. Adjust the rod until the clearance is the same between both the old set (MC/Brake booster) vs new set and should be good to go when installing into the car.