Comment by SaintSal

I thought of this too. The problem is that adding noise doesn't throw off the existing signals. All you can do is try to introduce new patterns, like try to convince the linear regression that you're left-wing and right-wing. Random data won't do that though; you'd need to know what patterns to recreate. A lot of effort, and as you say, pretty paranoid given one could just optout and block web trackers.