There is no need to worry about aliens destroying the Earth, we're perfectly capable of doing it ourselves.
The fact that we still exist is strong evidence that there are no billion year old highly xenocidal species out there as there are a number of ways (beserker Von Neuman probes, a Niccol-Dyson laser, ect) in which they could simply wipe out all life-bearing or potentially life-bearing planets in their local group of galaxies in less time than any intelligent species could get to the point where they started transmitting
Just because Faster Than Light drive might exist, we tend to conclude that any hostile aliens will have immediately paved the galaxy. But, as Douglas Adams noted space is vastly, hugely, mind-bogglingly big and FTL travel is likely really, really expensive in resources. I think if FTL was that easy, apart from its expense in resources, then there would literally be advanced aliens everywhere, if they exist at all. There is not much evidence suggesting that is the case, unless we are being kept in some zoo. (highly speculative but being kept locked in a interplanetary cage with a "do not agitate sign", seems appropriate to our species at times.)