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This is basically the equality checker that fulfills my requirements (but again, I don't need an equality comparer, I need a hash equality-comparer)

Update:

This is basically the equality checker that fulfills my requirements (but again, I don't need an equality comparer, I need a hash equality-comparer)

Note that this EqualityComparer is a private class and is only meant to serve the purpose of this specific HashSet which is not exposed at all.
In fact I don't also really care about the Equals, but rather about the GetHashCode, so I know whether an object with my specs have already been added to a HashSet. What can happen if I keep the Equals unimplemented? Does HashSet ever call it?

Note that this EqualityComparer is a private class and is only meant to serve the purpose of this specific HashSet which is not exposed at all.
In fact I don't also really care about the Equals, but rather about the GetHashCode, so I know whether an object with my specs have already been added to a HashSet.

public override bool Equals(ITrackableObjectData x, ITrackableObjectData y)
{
  if (x == null)
    return y == null;
  else if (y == null)
    return false;
  else if (x.TypeName != y.TypeName)
    return false;
  else
  {
    if (x.Id == null)
      return y.Id == null;
    else if (y.Id == null)
      return false;
    else
    {
      int xId = x.Id.GetHashCode(),
          yId = y.Id.GetHashCode();
      if (xId == 0 || yId == 0)
        return x.Equals(y);
      else
        return xId == yId;
    }
  }
}

public override bool Equals(ITrackableObjectData x, ITrackableObjectData y)
{
  if (x == y) return true; //ref eq.
  else if (x == null)
    return y == null;
  else if (y == null)
    return false;
  else if (x.TypeName != y.TypeName)
    return false;
  else
  {
    if (x.Id == null)
      return y.Id == null;
    else if (y.Id == null)
      return false;
    else
    {
      int xId = x.Id.GetHashCode(),
          yId = y.Id.GetHashCode();
      if (xId == 0 || yId == 0)
        return x.Equals(y); //use default eq.
      else
        return xId == yId;
    }
  }
}