Are hemoglobin molecules the same in different human populations? Why?

No, they are not the same. Every human population is prone to some mutation. The type of mutation depends on many factors: climate, temperature, terrain, type of food, and so on. Moreover, these mutations are inherited, which further increases the chance of a new mutation emerging. For example, in representatives of the Negroid race, the mutation is primarily due to the climate, low living standards (that is, unsanitary conditions), and nutrition. Asians will have very different mutations. So it is with hemoglobin. For example, people living high above sea level will have lower hemoglobin levels than people living in the plains.