I consider myself aware of the concepts of threading and why certain code is or isn’t “thread-safe,” but as someone who primarily works with ASP.NET, threading and thread safety
There are different levels of ASP.NET Developers. You could make a perfectly fine career as an ASP.NET Developer without knowing anything threads, mutexes, locks, semaphores and even design patterns because a high percentage of ASP.NET applications are basically CRUD applications with little to no additional business logic.
However, most great ASP.NET Developers which I have come across aren't just ASP.NET Developers, their skills run the gamut so they know all about threading and other good stuff because they don't limit themselves to ASP.NET.
So no, for the most part ASP.NET Developers do not need to know about thread safety. But what fun is there in only knowing the bare minimum?