Y'all, she did not just kill a person and it has nothing to do with the youkai's gender. The salt guy was already dead and was being puppeteered by a youkai. Plus a very influential person suddenly being possessed by a youkai would definitely disrupt the balance of Gensokyo. Exterminating it immediately was the most reasonable thing she could have done.
I do wonder how she did it though. Given how people think he just died normally, Reimu must have been pretty covert with it.