Hearing, unless you have a hearing problem, you hear the noise. For many they actually feed off the noise. They love it! It actually helps them perform better. At the same time others might be intimidated by a large crowd.
I think if you ask any athlete what they prefer... A very small silent crowd or a very large loud crowd, they would choose the big, loud crowd.
Sure the loud crowd can have a negative effect on performance at times. It can make communication more difficult. That is why many football teams will pipe loud noise into their practices. Loud noise can cause collisions between baseball players. Athletes must learn how to deal with noise and negative comments. Obviously Johnny Manziel flipping the bird was based on something he "heard".
I think when athletes say they don't hear anything, they just mean they can deal with it, it doesn't cause loss of focus, or keep them from getting the job done.
Regarding the Little League type of noise from the big crowds. It is a much different, more supportive type of noise. It would be great if all big crowds were that nice and simply cheered for their team. Unfortunately, that changes at the high school level and changes a lot more at the college level and even a lot more at the professional level.
Now if someone believes they can perform better with ear plugs, good for them. I think most actually use the noise to perform better. Other than golfers!