The SMP / multithread design has several levels in the ALSA project codebase. The kernel drivers are fully SMP / thread safe. The alsa-lib was designed to allow grouping of commands for returned handle to optimize pthread locking. The snd_*_open() calls are thread safe. The use of returned handles must be serialized in the application using own locking scheme. Standalone (not handle related) functions in alsa-lib should be fully thread safe.
There are a few global variables that are used in alsa-lib, such as the global error handler pointer and the global root config pointer. Accessing / modifying these would be thread-unsafe.
If you find a bug in kernel or alsa-lib which breaks these rules, please, let us know.