This is clever. I also note that "anywhere in the content of your religion" does not prevent you specifying "500 years" in some religion or society other than the bet one. For example you could found Kooky Belief Island (the religion subject to the bet), and then found Science Island with express instructions to go forth and illuminate the world after 495 years, Kooky Belief Island gives up their religion after being exposed to the ideas of Science Island. The main problem is the intent of the question is that the religion should self-destruct - nevertheless it's a clever way to cheat.

This is hilarious. The only problem is in my experience adult Cicadas aren't big eaters. They live underground for many years, then dig to the surface, make a god-awful racket for a few weeks, then die. Their adult phase is devoted to breeding mainly using stored energy and as adults they probably cause no more damage to the plants than they were already causing in their nymph stage. They just drink sap from branches instead of roots. However the sheer noise in year 500 might be enough to persuade people to give up the cicada god. "Okay this religion used to be funny, now it's beyond a joke!"

@Burki A religion is more than a person who believes. It's a whole movement of people. An apocalypse would be enough to end that movement in a pretty convincing way. If a new movement starts afterwards, it's a new religion - inspired by the old one maybe but not the same - and a post-apocalypse religion would be operating under different premises, they are "the people who missed the boat". In any case I'm exploiting the "No true scotsman" fallacy, a true believer kills themselves during the apocalypse, anyone who doesn't is no true believer, Q.E.D. It might be enough to win the bet :).

As I noted in another question, in accordance with Impact Depth en.wikipedia.org/wiki/Impact_depth, the atmosphere is good for maybe burning up a light rocky asteroid with a 5m diameter, anything larger than that has enough momentum to plow through the atmosphere and hit the ground. You would need to break the asteroid into at least 10 billion equal sized pieces, breaking it into merely a million or 10 million pieces would just make the problem much worse. Breaking up a 100m asteroid? Maybe practical. A 10km asteroid? No way.

@CeesTimmerman The Earth's atmosphere can stop a ~5m stony asteroid. (en.wikipedia.org/wiki/Impact_depth#Applications), this asteroid is 10-14km in diameter. If you blasted it into literally 10 billion pieces then the atmosphere could stop the pieces (but you would have 10 billion nuclear-yield blasts exploding in the Earth's atmosphere which may not be a good thing). Splitting it into dozens of pieces would mean nothing - they would still be millions of times more massive than the atmosphere could stop.

As noted by @ch7kor this answer is seriously flawed, the calculations are roughly correct, although by mass the atmosphere is actually 23.3% oxygen (20.25% is by volume) meaning it should be 1.50x10^18kg - that is minor though. Somehow, 1.32x10^17kg gets expressed as "13 thousand metric tonnes" when it's actually "130 thousand billion metric tonnes", or roughly 2 million years of current global hydrogen production.

@Roughcoat Well the possible locations are Earth-Sun L1 point, in orbit around Earth, or high altitude balloons. The L1 point will offer the most comprehensive shading, as other shading solutions will only shade at best 50% of the time. The cheapest would be high altitude balloons, but they might get shot down... Surface wont work well because both nature and people will rip the shades up and destroy them.

@HSquirrel triggering a runaway greenhouse effect is the obvious alternative to snowball earth, and I considered it too. One problem is it would take a damn long time to melt Greenland and Antarctica making the polar latitudes a safe haven - the thermal mass of the ice will locally counteract the warming for a long time. In a sense, Antarctica gives us a head start on creating snowball Earth.