Let me put it this way: if you really want to satisfy the rapture believers' goals in a non-exploitative way, why not just do the pet service insurance in exchange for a share of their estate in the event of he rapture?
Remember, folks, whenever you see yourself "tough-mindedly" agreeing to something that also happens to be self-serving, you're obligated to follow these steps:
1) Look for a less problematic middle way.
2) When you find it, advocate that instead.
Easy steps, but rarely done.
By this reasoning, shouldn't a life insurance company be willing to sell you life insurance and defer the premium paid until you die?
http://eternal-earthbound-pets.com/Home_Page.html
Providing assurance that pets will be provided for in the event of Rapture.
Having thought it over, I'm OK with the ethics of this service.