In the olden days of 1990, when the original Rifts rulebook was published, the world of Rifts was what would now be described as a "points of light" setting: tiny dots of civilization trying to scratch out an existence in a vast, monster-infested wasteland. There were a few cities that had managed to restore old technologies, but most of North America (and indeed, the world) was a howling wilderness, depopulated and dangerous. Much of the early artwork for the game -- particularly the work of Larry MacDougall, shown above -- supported this "scorched Earth" interpretation.
However, there was never really much mechanical support for this style of play. There were some character classes, or O.C.C.s (to use Palladium's terminology) that fit in with such an interpretation, including the Wilderness Scout and Vagabond, but others, like the Cyber-Doc and City Rat, supported a more cyberpunk interpretation. Even more plentiful were high-tech warriors like full-conversion 'Borgs, Glitter Boy Pilots, and Juicers. Though not explicitly delineated in the text of the original rulebook, over time, typical Rifts characters were implied to be something like a cross between the heavily armed mercenaries of Shadowrun and Cyberpunk 2020 and superhero teams. You could certainly play out smaller, more personal conflicts, but the published material set up big villains like quasi-Lovecraftian "supernatural intelligences", the evil Federation of Magic, the oppressive, Nazi-esque Coalition, the alien Mechanoids, and even the Four Horsemen of the Apocalypse for your characters to take down, either for money or out of a sense of justice.
Over the years, more and more high-tech wonder weapons were introduced into the setting, usually with each one being more powerful than the last. Mecha began to incorporate gee-whiz science fiction gear like force fields and jetpacks. By the time of Rifts' new core rulebook, the Ultimate Edition (released in 2005), the cyberpunk-meets-superheroes nature of the game was fairly evident. The book is filled with artwork of characters of superheroic proportions, drawn in a style reminiscent of mainstream comics of the 1990s. (Some artwork is recycled from early publications, with the game's author, Kevin Siembieda, specifically saying that he wanted the book to incorporate what he considered classic Rifts art along with some new pieces. Tellingly, few of MacDougall's gritty illustrations made the cut.) The first piece of artwork the reader encounters in the Ultimate Edition is a full-color, Blade Runner-style cyberpunk metropolis. More recent Rifts sourcebooks, like Black Market and Northern Gun, have continued the trend toward an ultra-high-tech world:
Rifts is a lot of things, but I wouldn't call it a post-apocalyptic game. The world may have been laid to waste by an apocalyptic event several centuries in the setting's past, but there's no scrounging for food, digging up old technology, or radiation to be found. It might be cyberpunk, or science fantasy, or superheroic, depending on what elements you want to emphasize. At the end of the day, it's just Rifts. You could make it into a post-apocalyptic game, but it'd take a lot of work. You'd probably be better off looking elsewhere.