I don't know why but it just doesn't work.
I don't have a lot to say but I hope someone knows a workaround.
I reproduced everything I did outside the Viewport and it works, but I need it in the Viewport because that's where my Game itself is running.
You have to proxy the events and send them to the next level. Put this on the main script (like on the root node of the scene) assuming your viewport variable is called viewport (just edit that if you have a different variable name).
func _input(event):
if viewport and is_inside_tree():
viewport.input(event)
func _unhandled_input(event):
if viewport and is_inside_tree():
viewport.unhandled_input(event)
func _gui_input(event):
if viewport and is_inside_tree():
viewport._gui_input(event)cybereality
This seems to be given the right Input Variables, but the Click still isn't getting recognized.
I attached it to the MainScene in my Case "GameWindow" where the Viewport with some UI is contained.
I'm not sure, that worked for me. You might have to check some of the mouse flags on the controls to see if maybe something is blocking the click.
cybereality
I just use the Mouse Filters now without the code you provided and it seems to work now.
Thank you for helping me 
Great, it worked!