The major friction that opposes a car during acceleration is the kinetic friction. It is known that friction opposes the movement of an object or opposes motion. There are actually different kinds of friction, such as kinetic friction, sliding friction, static friction, and probably more.
These different kinds of friction act on objects at different stages of motion. Understand that friction is a force, usually referred to as frictional force, and it is of a different type. So, when a car is in motion, the frictional force that acts in opposite to its direction is the kinetic friction.
The frictional force that acts both in the direction and opposite of the accelerating car is the static friction. There are basically four forces that affect a car, which are thrust, drag, lift, and weight. In conclusion, I think the largest friction that opposes a car is static friction because it is employed in the application of brakes.