Let variable x_i represent topping i. True means topping is on the pizza, false means it is not. This is the boolean choice. Customer wants "+i +j": that is the clause x_i OR x_j. Customer wants "+i -j": that is x_i OR NOT x_j.
Customer wants "-i -j": that is NOT x_i OR NOT x_j. Each customer gives you one clause. You have m clauses total over n variables. This is a standard -SAT instance ready to solve.