No, it is not taking away any of your rights. You still have all the same rights.
The access to the content requires additional work, that is all. The fact that you still have your rights is what allows you to request that access for whatever situation you're in.
So if I lock you in a room, I am not taking away any of your right to go where you choose ? It's just your "means of getting there" that are somewhat limited and those aren't protected by law.
And yes, that's exactly how insane you sound. If you limit my "access to my rights" you have definitely taken away those rights. Stop spouting bullshit.
The access to the content requires additional work, that is all. The fact that you still have your rights is what allows you to request that access for whatever situation you're in.