Mutexes aren't OK even if you only use one. They are error prone, you can forget to unlock. And of course, there is a temptation to avoid using it for efficiency reasons, because you "know" this part of the code is safe.

These days I develop servers on the JVM. We almost never think about mutexes or related things, libraries take care of that. I use Scala, and our entire data model is immutable, eliminating most race conditions. I think I had to declare something as volatile once or twice.