The class itself doesn't have any culture as such. It's the thread that accesses this class that has a culture and the thread's culture is used in a class (static or not).
Static really refers to how the class's state is shared across different threads. Your static class can be stateless (i.e. it doesn't store an data, often the case with helper type of static classes) which will create less problems for you.
If you store any state in your static class, you have to be careful for 2 reasons:
in general, it's harder to control access to statically held data in a multithreaded environment,
if any data you store is culture-specific, you may have problems with interpreting this data when using threads with different culture.