How to check if property setter is public

Check what you get back from GetSetMethod:

MethodInfo setMethod = propInfo.GetSetMethod();

if (setMethod == null)
{
    // The setter doesn't exist or isn't public.
}

Or, to put a different spin on Richard’s answer:

if (propInfo.CanWrite && propInfo.GetSetMethod(/*nonPublic*/ true).IsPublic)
{
    // The setter exists and is public.
}

Note that if all you want to do is set a property as long as it has a setter, you don’t actually have to care whether the setter is public. You can just use it, public or private:

// This will give you the setter, whatever its accessibility,
// assuming it exists.
MethodInfo setter = propInfo.GetSetMethod(/*nonPublic*/ true);

if (setter != null)
{
    // Just be aware that you're kind of being sneaky here.
    setter.Invoke(target, new object[] { value });
}