Hi Maria!
There are special events for Independence Day at Disney!
Last year there were special fireworks and special characters like Betsy Ross and Benjamin Franklin!
The thing about Extra Magic Hours is that when the magic hours are up, it makes the park more crowded!
And whenever there is a big event like special fireworks for the 4th of July, that park will be the most crowded! So, Magic Kingdom will definitely be the most crowded on Independence Day.
So, my suggestion is to check out touringplans.com. They have tons of info about crowd predictions. You can see which days will be the most crowded and which parks to avoid. Then you'll just have to decide if it's worth it to you. I would really want to see the special fireworks, so I'd probably spend the day at Animal Kingdom and then hop to Magic Kingdom for the fireworks. Sometimes when it's crowded, the park hopper is your best bet! That a decent idea of what you want to see in the parks!
I hope that helps! You will have a magical time, crowds or not because holidays are DOUBLE magic at Disney!