As in Aldnoah.Zero and Assassination Classroom, the moon has it’s long standing in anime as something that gets blown up LOTS of time. In truth, the moon is simply TOO big to be blown up or easily destroyed.
In a CBC Quirks and Quarks Q&A, the moon has been hit time and time again by asteroids and still there. Any impact that could produce something that could reach Earth would simply burn up in the atmosphere. With the asteroids already mapped there isn’t anything out there that could pose a risk to the moon.
So if you’re watching anime and the moon blows or has been blown up … take it with a grain of salt.