Assert an Exception using XUnit

The Assert.Throws expression will catch the exception and assert the type. You are however calling the method under test outside of the assert expression and thus failing the test case.

[Fact]
public void ProfileRepository_GetSettingsForUserIDWithInvalidArguments_ThrowsArgumentException()
{
    //arrange
    ProfileRepository profiles = new ProfileRepository();
    // act & assert
    Assert.Throws<ArgumentException>(() => profiles.GetSettingsForUserID(""));
}

If bent on following AAA you can extract the action into its own variable.

[Fact]
public void ProfileRepository_GetSettingsForUserIDWithInvalidArguments_ThrowsArgumentException()
{
    //arrange
    ProfileRepository profiles = new ProfileRepository();
    //act
    Action act = () => profiles.GetSettingsForUserID("");
    //assert
    ArgumentException exception = Assert.Throws<ArgumentException>(act);
    //The thrown exception can be used for even more detailed assertions.
    Assert.Equal("expected error message here", exception.Message);
}

Note how the exception can also be used for more detailed assertions

If testing asynchronously, Assert.ThrowsAsync follows similarly to the previously given example, except that the assertion should be awaited,

public async Task Some_Async_Test() {

    //...

    //Act
    Func<Task> act = () => subject.SomeMethodAsync();

    //Assert
    var exception = await Assert.ThrowsAsync<InvalidOperationException>(act);

    //...
}