It really makes me wonder if the sins of your past changes your form when the people enter hell. Like if all the furries in hell took on those anthropomorphic animal people forms. Just a guess though

In the 1920s.
However, while I like this headcanon, I think their personalities are too different. Facilier is a con-artist by trade, while Alastor is more of a showman who does what he does for the sake of chaos (although he probably has more complicated motives in mind for the hotel).