Let us call this abstract religion Zargism. So why are people Zargists?
Carrot: if you are a good Zargist you will go to heaven after you die (regardless of if that's at the end of the world or not).
Carrot: being a member opens up job opportunities.
Stick: if you /aren't/ a good Zargist, you will burn in sulphurous fire after you die.
Stick: at many times in history and in many places, if you aren't a good Zargist, the state or power of the Church punishes you, or you just suffer from anti-your religion bigotry.
Bluff called: the end of the world hasn't happened yet, and despite lots of prophecies about it, it keeps on not happening. So why worry?
Other aspects of the religion: as well as the bit about God ending the world, Zargism comes with a basic moral package structured around helping other people, not hurting other people. That's quite appealing (actually I think the appeal lies in wanting /other/ people to follow the moral code so they're nice to you and don't hurt you rather than constraining yourself to behave well, but anyway there's an appeal to being part of a movement where everyone is following a code that prohibits them from being unpleasant to you).
Belief in belief. Lots of people believe they believe things that they actually don't believe at all. They don't realise the difference between belief in something (the unshakeable conviction that something is true regardless of lack of proof or counter-evidence) and thinking that it's good to believe something. This explains religious types who fervently preach against sin and the eternal damnation that will inevitably follow while themselves committing all manner of sins. Either they're looking forward to a nice long brimstoney bath or they don't actually believe what they think they believe.
Personality. There are plenty of apocalypse cults based on the hypnotic personality of the founder and a few brainwashing techniques. Whether these scale well beyond a number that the founder can have direct control over is a good question.
Scope. Perhaps this god's remit goes beyond destruction. The Hindu god Shiva has both destructive and benevolent aspects, for example. One of my favourite fictional gods is Morian of the Portals, from Guy Gavriel Kay's novel Tigana. Morian is the god of change. Every choice you make in life, every door you pass through (or don't) is a choice that cannot be undone, and a portal of Morian. Death is such a portal, but so is birth: Morian's remit therefore covers both creation and destruction.
Belief that this world is an aberration. If the belief system is constructed such that this world represents a nasty, brutal aberration from the perfect void into which our poor unfortunate souls have been drawn, then the world-ending god of destruction becomes the saviour who will return us to the perfect void. After all, while the apocalypse is generally portrayed as horrific and violent, such a god could presumably make it instant and painless, and a welcome return to the state of bliss.