After a bit of research, it seems clear to me that - except in exceedingly rare, if not totally nonexistent circumstances - the laity ought not take communion at an SSPX chapel, or otherwise formally participate in the illicit liturgy. That the priests themselves ought not administer or say the illicit Masses is given in that they are illicit, this fact being confirmed by multiple sources, one binding, one traditionalist.
 
    The argument itself is straightforward: The Church has spoken specifically to this matter in an interpretive fashion, and authoritative interpretation have the same force as the law itself, if not universally, at least in respect to particular cases. This is a particular case that has been spoken on, however, so the Church’s interpretation of the law is binding.
 
The interpretation:
From STATUS OF SOCIETY OF ST PIUS X MASSES, Commission Ecclesia Dei:

 
Why the interpretation is necessarily binding:

Nor is this solution repugnant to all notable traditionalist sources:
Fr. Z's take on it:

The referenced canon:

    Traditionalists will argue that a true spiritual advantage suggests it. Note, however, that it has been clarified with binding authority that "the fact of not being able to assist at the celebration of the so-called 'Tridentine' Mass is not considered a sufficient motive for attending such Masses."

    In more general terms, for any action to be moral, the object, circumstances and intent must all be acceptable. (Moral Theology 101) From this arises the generally accepted fact that anyone can attend even a protestant service so long as he does not formally participate in it (the object of the action), so long as he does not cause scandal (the circumstances of the action), and so long as he does so for a genuinely good reason (the intention of the action), and the same can be said of attending an SSPX Mass. Protestantism is further removed, so it makes sense that what we can do in regards to their services, we can also do in regards to SSPX's Masses. That the intention can be good need not be visited.

    For the object of the action to be morally acceptable, either he must be incapable of morally or physically participating in a licit Mass, or else he cannot formally participate in an SSPX Mass. In that taking communion does constitute formal participation (Lest there be any doubt, this is what the cited canon referred to specifically, for the sacrament itself is illicit), a person cannot licitly receive the sacrament unless it is morally or physically impossible to receive it licitly elsewhere.

    In regards to the circumstances, scandal must be avoided, schismatic attitudes and indifferentism must not be allowed to take root. The latter especially seems that it would be difficult to satisfy. When something is done often enough out of preference, the distaste for what it lacks (in this case licitness) is numbed, leading almost necessarily to an attitude of indifferentism in regards to whether a sacrament or liturgy is licit.

    Is it not fitting after all, that the Sacrament called "Communion" should be received in full union with Rome?

    Can brevity lead to ambiguity? Yes. But given a colorful vocabulary, articulately employed, it need not. When brevity is lost, however, interest is lost, and only a select few will actually retain anything, or even read until the end of the post.

Brevity is the Soul of Wit - William Shakespeare

    The other day it occurred to me that a blog post on matrimony would not be amiss... There are all too many people that encourage only looking into the priesthood and the consecrated life, without encouraging young men or women to pray about matrimony, and I have recently encountered "Catholics" who are absolutely convinced that marriage is harmful to the spiritual life, but, as it were, a necessary evil. This is erroneous, fallacious, and dangerous. This conclusion is reached because the fact is acknowledged that the consecrated life is a higher calling than matrimony. (This is what the Church has said all along, so I won't get into it in any depth now, maybe later.) If this is true, it must be better for attaining salvation, and so a married person has given up his best shot at getting to Heaven. However, a vocation is that state in life for which a person is made. Practically by definition, it is through a person's vocation that the best and surest rout to Heaven is for that person. If you are one of those persons for whom I am writing this blog post, you're thinking right now: "Clearly, there is a contradiction... he just said that the best vocation is the consecrated life, but that the best vocation for anyone is their own vocation and that many people are not called to the consecrated life." So please, if you see this apparent contradiction, bear with me.
    The religious life may be a higher calling than the married life, but the married life has a wholly different kind of glory. Only the consecrated life requires perpetual virginity, but marriage is still a sacrament which includes literally the fulfillment of chastity. Whereas the consecrated life takes a human faculty that brings joy and offers it to God pure and unused, matrimony takes that same faculty and uses it unto the end for which God made it. The sanctification of this faculty involves chastity, ordered to the love of the spouse and the good of the children; because marriage is so good, the abuse of chastity is so wrong. The consecrated life is a way of rising above our fallen nature in order to be brought as close to God as is possible in this life; marriage raises our fallen nature up, and brings it closer to what it was supposed to be in the beginning, when God blessed man and woman, and said "Be fruitful and multiply". In the one you may spend your whole life living God and praying to God for your fellow man, but in the other you devote your life still to God in a different mode. In the cloister you pray to God that the right people may come into the lives of sinners that they might convert; in matrimony you are on the front lines, coming into the lives of people and being used by God for the sakes of the sinners. In the cloister a person prays that good parents may give birth to and raise children to be the next generation; when you are married, you receive the graces from these prayers, because you are those parents.
    It is only in matrimony that procreation is permitted because matrimony was made to sanctify the only way that humans can procreate. In this sacrament, a couple becomes a mother and a father, through mirroring God's trinity in the best way humanly possible: In matrimony two become one, and from their loving oneness children spring forth. A wise man once said that lust is wrong not because a person takes too much but that he settles for too little. This is why. Marriage carries with it great responsibility, great graces, great love, great symbolism, great joy, and humanity in its fullest. 
    So why is it that the consecrated life can be both higher objectively and worse for a certain person? Because both are so good, because individuals are given talents ordered to their specific vocation, to make the most out of it that can be made out of it, and because goodness comes exclusively from fulfillment of a thing's purpose. Just as a good knife is the one that cuts well, a good man is he who fulfills his calling. When a man is called to marriage, he will be holiest when he is married.

       This is a counter-intuitive teaching. One would think that it would be more important to give God the highest form of worship, regardless of what others are doing, than to fit in with everyone else. St. Augustine does not seem to be of this opinion, however. In fact, he followed this passage immediately with the example that a person ought not to fast on Saturdays when in a community whose custom is not to fast on Saturdays. To fast is good by its very nature. Voluntarily accepting hunger in order to be more wholly detached from worldly pleasures and more totally given to God will bring us closer to God. This  counter-intuitive teaching is driven further by Augustine in Par 5, in which he speaks against the condemnation of one place’s custom as a response to finding an apparently better practice elsewhere, saying that such condemnation "would show a childish weakness of judgment against which we should guard ourselves, and which we must bear with in others, but correct in all who are under our influence."

       Although this clearly does mean that whether we follow a custom should chiefly be determined by what the community is doing, this is not a license to relativism. One practice may very well be better than another, but it is more important that we are humbly united in Christ under our bishops than that our customs are perfect. St. Augustine is not saying that no custom is better than another, but is saying that it is more important for a community to be united in a good worship than it is for an individual to perform the best worship. St. Augustine very clearly viewed acceptance of a custom by the universal Church to be authoritative proof that it is good (pars. 1, 5, 6, 8), going so far as to say, "If the universal Church follows any one of these methods, there is no room for doubt as to our duty; for it would be the height of arrogant madness to discuss whether or not we should comply with it." (Par 6)

       We can learn from St. Augustine our proper place as the laity in regards to disciplines of the Church. We ought to abide by local customs, even when another custom may be better, for the sake of unity. Acceptance by the universal Church authoritatively proves a custom to be good, to such an extent that St. Augustine referred to mere discussion of whether we ought to comply with it as "the height of arrogant madness". We ought to accept the disciplines of the Church then with docile humility, only going beyond the customs when doing so would not be disruptive.