"The rationally necessary is not necessarily the objectively real"
is itself either rationally conceivable or not. If it is not rationally conceivable, then it is meaningless and the objection vanishes. If it is rationally conceivable and intelligible, then it must be either a statement about what is objectively and actually the case or not.
If the statement is not objectively and actually the case, it is false and the objection collapses again.
But if it is objectively and actually the case, then it is still false, since it claims that what is rationally necessary is not necessarily actually the case.
Moreover, is that statement itself "rationally necessary"? Even my slowest readers should be able to get this point.
Thus the objection is self-contradictory in several senses.