I see no reason to say that stalking laws are a violation of due process. Due process simply means that a person who is accused of a crime must have their "day in court" and that they cannot be punished unless they are convicted of that crime. Stalking laws do not deprive the accused of due process. There is no provision in stalking laws to say that a person can be fined or jailed or anything like that without trial. Therefore, there is no conflict between stalking laws and the right to due process.
Due Process is not a law, therefore it can not be abrogated simply by the enactment of a statute.
Due Process in more simpler legal terminology is, what Process is the person Due. When it is reversed, it makes clearer sense.
Although yes, a law can be challenged as a violation of the DP clauses (5 or 14), Stalking is a law that protects society, such as Menacing.
The "Process they are Due" is stated in the other post.