Today I got this error dialog when trying to open a solution "The project file '....csproj' cannot be opened. The project type is not supported by this installation." Visual Studio went on to display all the projects in the solution it could, except the website project.
Googling this returned this helpful post:
Indeed, reading the 5th post on that thread lead me to deleting the ProjectTypeGuids element from within the first PropertyGroup element. Hitting Reload Project in Solution Explorer showed the project correctly.