But conquering fear IS important. Fear is, after all, what stops us doing so many things. It's the little voice that makes years go by until you look back and see missed opportunities, timid decisions, situations we just opted, at some point, to settle for. This applies to just about every career I can think of, every life I can think of.
Including that of a screenwriter! Now, I can't claim that this is the same for everyone, but the screenwriting-related things I have the fear for are: pitching (to anyone) and networking (I'm very hit or miss with this). I'm okay expressing my ideas in writing, but verbally, it's a different story. It doesn't help that I think faster than the capacity of human speech - and I talk pretty fast.
So what's the answer? Well, it's fairly obvious that if you fear something, you probably need to go ahead and do that very thing. Just do it, as some adman for Nike said. Pitching is slightly easier as you can practice in advance in front of a camera (or family). To cope with networking, I recommend an excellent book called Good in a Room. As with pitching, this ultimately comes down to lots and lots of practice. Go to lots of events and talk to lots of people. Eventually, you'll stop being a gibbering idiot.
Remember, to conquer fear, you.... just do it.