I created a new ASP.NET MVC project and implemented a site authorization filter.
When I map the routes to the {controller}/{action} pair, I pass a role
Actually, George is right. MVC Routing respect ordering route. Your last route must be generic as possible, and your previous route must be specific as possible.
In your case, both are generic. You should
MapRoute("SomeAction", "Post/{action}", new {controller = "Post", role = "User");
and then
MapRoute("Default", new {controller="Home", action="Index", role = "Anonymous"});
so, you give specificity to both routes.