The cost of auto insurance is based on a variety of factors, including the nature of the vehicle and the characteristics of the anticipated drivers.
The manner in which you have phrased your question concentrates on the car itself. A 2-door car is more likely to be characterized as a sports car and therefore, may be within a rating category that results in a higher premium.
An insurance "rate" is the cost per unit of insurance, Therefore, generally speaking, the premium is the product of the rate multiplied by the amount of coverage. Keep in mind also that insurance rates are, for the most part, regulated by the states. The goal of rate regulation is to reach a balance between affordability for the consumer and ensuring that the insurer collects sufficient money to pay expected claims.
All of that said, while it is not a universal truth that a 2-door car will be more costly to insure, it may well turn out to be the case depending upon how the insurance company categorizes it in its filings with the state insurance regulator.
In most cases yes your car insurance will be higher because a 2 door is considered sporty and a 4 door is considered a sedan or family car. I know that when we had a Honda Civic and a Honda Protegee, the same year cars, about the same mileage, the Protegee was about $175.00 more a year. The registration will also be higher in a 2 door vs a 4 door.