C# public variable as writeable inside the class but readonly outside the class

Don’t use a field – use a property:

class Foo
{
    public string Bar { get; private set; }
}

In this example Foo.Bar is readable everywhere and writable only by members of Foo itself.

As a side note, this example is using a C# feature introduced in version 3 called automatically implemented properties. This is syntactical sugar that the compiler will transform into a regular property that has a private backing field like this:

class Foo
{
    [CompilerGenerated]
    private string <Bar>k__BackingField;

    public string Bar
    {
        [CompilerGenerated]
        get
        {
            return this.<Bar>k__BackingField;
        }
        [CompilerGenerated]
        private set
        {
            this.<Bar>k__BackingField = value;
        }
    }
}