No, never. The processes are well isolated; each process runs in a separate isolated address space. On advanced processor
architectures usually used for Windows systems (x86, x86-64, IE-64), this is the hardware protection at the level of CPU. If the processes are of the same application, it does not matter.
Besides, any possible clashes (inside the same process) can really happen and are associated with static fields or properties, in other words, with something where you share the same memory location. It has nothing to do with static methods. You simply don't quite understand what are they. They are just similar to "usual" non-OOP functions/procedures, in contrast to
instance methods. In instance method gets an implicit "this" pointer (reference, managed pointer, in case of CLI), which references some instance of your type, so you can access other instance members of the instance. A static method does not get this reference and cannot access any instance. That's it.
Please see my past answers on static methods vs. instance methods:
Type casting in c#[
^],
C# windows base this key word related and its uses in the application[
^],
What makes static methods accessible?[
^].
—SA