Many contractors routinely use drywall screws to mount cabinets. Does that mean it is safe, not really. This is not due to any attempt to increase profits on their part as the cost of the screws are not terribly different but rather due to a lack of knowledge and the convenience of using what is more commonly at hand.
The problem with Drywall Screws is that they are very brittle and should not be used where weight bearing is an issue. They are most likely adequate for mounting the cabinets themselves, but can become a problem when weight is placed in the cabinets. The danger is not that the screws will pull out from the wall but rather that it will actually break or "shear off" as the result of a sharp jolt to the cabinet or degrade over time due to the stress from bearing weight.
Here in California the concern is that an earthquake could bring the cabinets down. Failures are rare but have occurred in situations such as when heavy china dishes are stacked, filling the cabinet or when shelves are overloaded with canned goods or other weighty objects. The problem is that even if you were to conclude that your cabinets will never hold a tremendous amount of weight, years will go by and you will forget about the drywall screw situation and who knows what the cabinets will be used for then.
As a way to ensure that you have no future calamity it is advised that you leave the drywall screws in place and also reinforce the mounting by adding some cabinet screws alongside the drywall screws. This will give you all the peace of mind you need and is much easier than removing and replacing all the drywall screws. Make sure that you are putting the screws into the studs of the wall. you should be able to use the drywall screws as a guide to do this.
