The decree of excommunication is a legalism only. It is morally a nullity. This is why the SSPX can move forward with equanimity. It knows there is no real truth behind the accusations. Here are the words of the 1913 Catholic Encyclopedia:
"Excommunication is said to be unjust when, though valid, it is wrongfully applied to a person really innocent but believed to be guilty. Here, of course, it is not a question of excommunication latæ sententiæ and in foro interno, but only of one imposed or declared by judicial sentence. It is admitted by all that a null excommunication produces no effect whatever, and may be ignored without sin."
Notice that the encyclopedia does not include a latae sententiae in this explanation PRECISELY because it is an internal matter--in foro interno--which no one on earth may interpret except the individual in the forum of his own conscience. But if the Pope's motu proprio is interpreted as a legitimate judicial sentence--as you are claiming--then the explanation would apply, i.e., the excommunication produces no effect and may be ignored without sin.
The 1983 Code contains provisions for ecclesiastical authority to declare a latae sententiae excommunication has been occured. Do you accept these provisions?
Can. 1331 §1 An excommunicated person is forbidden:
1° to have any ministerial part in the celebration of the Sacrifice of the Eucharist or in any other ceremonies of public worship; ...§2 If the excommunication has been imposed or declared, the offender:
1° proposing to act in defiance of the provision of §1, n. 1 is to be removed, or else the liturgical action is to be suspended, unless there is a grave reason to the contraryCan. 1342 §1 Whenever there are just reasons against the use of a judicial procedure, a penalty can be imposed or declared by means of an extra-judicial decree; in every case, penal remedies and penances may be applied by a decree.
Another important criticism I received concerns the question of the possible invalidity of the declaration of excommunication issued by the Congregation for Bishops. A couple of well-versed canonists pointed out something crucial which I neglected to include in my thesis, and which probably led to an incorrect inference on the part of many readers: once the competent authority in the Church, in this case the Congregation for Bishops, has publicly declared a latae sententiae (automatic) penalty to have been incurred, the persons named in that declaration are bound to submit to the public effects of the penalty.
They are not free to simply ignore the penalty, alleging reasons why it does not apply to them. They may be sincerely convinced that the penalty was not incurred automatically. They may be convinced that the declaration was invalid. They may even be able to prove their case. But they cannot simply assert this, and then act as though there had been no declaration of excommunication. They must prove their case in an administrative recourse. If they choose not to lodge a recourse, then the matter rests as established by the competent Church authority. They are excommunicated. (Fr. Gerald Murray, Letter, Latin Mass Summer 1996)
And what does whole paragraph on unjust excommunication say?
An excommunication is said to be null when it is invalid because of some intrinsic or essential defect, e.g. when the person inflicting it has no jurisdiction, when the motive of the excommunication is manifestly incorrect and inconsistent, or when the excommunication is essentially defective in form. Excommunication is said to be unjust when, though valid, it is wrongfully applied to a person really innocent but believed to be guilty. Here, of course, it is not a question of excommunication latæ sententiæ and in foro interno, but only of one imposed or declared by judicial sentence. It is admitted by all that a null excommunication produces no effect whatever, and may be ignored without sin (cap. ii, de const., in VI). But a case of unjust excommunication brings out in a much more general way the possibility of conflict between the forum internum and the forum externum, between legal justice and the real facts. In chapter xxviii, de sent. excomm. (Lib. V, tit. xxxix), Innocent III formally admits the possibility of this conflict. Some persons, he says, may be free in the eyes of God but bound in the eyes of the Church; vice versa, some may be free in the eyes of the Church but bound in the eyes of God: for God's judgment is based on the very truth itself, whereas that of the Church is based on arguments and presumptions which are sometimes erroneous. He concludes that the chain by which the sinner is bound in the sight of God is loosed by remission of the fault committed, whereas that which binds him in the sight of the Church is severed only by removal of the sentence. Consequently, a person unjustly excommunicated is in the same state as the justly excommunicated sinner who has repented and recovered the grace of God; he has not forfeited internal communion with the Church, and God can bestow upon him all necessary spiritual help. However, while seeking to prove his innocence, the censured person is meanwhile bound to obey legitimate authority and to behave as one under the ban of excommunication, until he is rehabilitated or absolved. Such a case seems practically impossible nowadays.
So - unjust excommunications in the external forum DO bind, even if they are only declared (as having been incurred) and not imposed! See what it says "or declared by judicial sentence". It is a latae sentiatae which is declared, and a ferendae sententiae which is imposed.