I won’t take credit for this idea. It was posted on r/worldbuilding but was nuked by the mods for “asking for content”, as usual only after lots of interesting discussion.

OP: "I consent"

Other worldbuilders: "I consent"

The mod: "I don't"

My first thought is that such a scenario would lead to a rise of fascist governments as nations urge to prepare to fight back. These fascists invade their neighbors in hope that they could gather an equal army... somehow.

When 6 months pass and no aliens show up, the fascists whose entire existence was justified by this imminent threat start spreading disinformation about the aliens' message to ensure that their populace still believe in the promised invasion.

Eventually, the fascists exhaust their reserves (and their lies) and the War ends. The broken moon is forever associated with fascism and a conspiracy theory spreads that claims that the fascists themselves crippled our moon.