SDL offers several thread synchronization primitives. This document can't cover the complicated topic of thread safety, but reading up on what each of these primitives are, why they are useful, and how to correctly use them is vital to writing correct and safe multithreaded programs.
SDL also offers a datatype, SDL_InitState, which can be used to make sure only one thread initializes/deinitializes some resource that several threads might try to use for the first time simultaneously.