Threads (and atomics) are currently enabled, so long as you link SDL2 using the -s USE_SDL=2 switch rather than compiling from source. If you have a suitable browser (most desktop browsers now work, except IE and Safari) you can click on this link to run my BBC BASIC app, which is multithreaded and couldn’t work otherwise.
Nor me! Fortunately it’s all been done for us and it ‘just works’. 