I don't expect a conservative backlash, on the contrary Francis's Pontificate has weakened the conservative wing considerably. Given that 80% of the voting cardinals were appointed by Pope Francis, I would expect them to elect a successor that continues in the same direction, perhaps even a more radical one.

During his pontificate Francis also made a lot of efforts to bring in new groups into the corridors of power. Not only by his appointment of cardinals, but also e.g. by reforming the Curia with Praedicate evangelium.