Hello @BenjaRodriguez ,
For me I have one way to take out the Natura2000 layers. The first is to go to the attribute table and click one by one the rows that say Natura2000. After you click one layer, click the three horizontal lines that are on the top right side of the attribute table, then click center on selection, after you see that layer highlighted on the map, you can click that layer on the map and delete. Since you will be deleting this one by one its more time consuming. I'm sure there is an easier way, but that's how I usually do it. Remember to save after you delete all the features, so all of your work isn't undone.
Also wanted to say that that seems like a really interesting map you are doing.