Carlsbad7, let me suggest that your first statement is greatly overstating a minor point. Fear of making a mistake is primarily due to two things. First, personality. There are players , both sexes, that can shoot on goal 20 times and know that the next one will go in and not be worried about missing. This is the natural personality of certain positions, primarily forwards. Others (often more the perfectionists) that strongly desire to not make a mistake. They will refuse to shoot because every shot missed is considered failure. These personalities should be your defenders.Fear of making a mistake comes from always playing against high level competition.
In these type of situations wins and losses can all come down to a single player delivering on their responsibilities.
High level competition also forces coaches into player specialization which makes it easier to assign blame / fault if anything goes wrong.
Lather rinse and repeat week after week and you can see why players are more afraid to make mistakes than they are taking risks.
For Girls if a team can be consistent in how they play a position, and everyone trusts each other eventually they'll start taking risks. If risks work out and players don't get burned on position, they'll try being risky more and more often. Eventually they start playing like boys.
The second big influence is the treatment that coaches give from an early age. A huge component of good youth coaches is the ability to instruct in a positive manor. A business management principle is that for every negative thing said, four positive things should be said. Let me know if you have available coaches that fit this description. They are few and far between.
The level of competition played shouldn’t overly impact your level of fear. This may be an influence if you can’t compete at that level, but if you can’t compete and your team is always playing at this level, perhaps you should be on a different team where you can compete.