Ummm I guess it's a 'problem' if you suppose that (a) the Church Fathers give us generally reliable information about anything and (b) if you think that Clement is in the habit of telling us which heretics use which gospel. In the case (a) I do not subscribe to the silly 'Church Fathers as reliable researchers' model that most (religious) scholars put forward. At best they were hearsay experts. They usually say something like 'heresy X' used the Gospel of Matthew. I don't believe that every sect which is claimed to use Matthew actually used Matthew. It was a simple formula which had little value other than sound reliable.
But in the case of Clement in particular he rarely mentions the use of particular gospels among the heresies. In fact I would turn around and say that THE ONE gospel that Clement seems to be in the habit of identifying heretical practitioners for is the Gospel of the Egyptians. In Stromata 3 he starts chapter 5 by saying:
We have no intention of making a closer examination of this topic or mentioning more implausible heresies. We have no intention of being forced to an individual discussion of each of them in all their scandalous nature or prolonging these notes to a vast length. Let us answer them by dividing all the heresies into two groups. Either they teach a way of life which makes no distinction between right and wrong or their hymn is too highly strung and they acclaim asceticism out of a spirit of irreligious quarrelsomeness. I must first expound the former division. If it is legitimate to choose any way of life, then clearly it is legitimate to choose the way that involves asceticism. If there is no way of life which carries danger for the elect, then clearly this is particularly true of the life of virtuous self-discipline. If the Lord of the sabbath has been granted freedom from accountability for a life of licentiousness, the man whose social life is orderly will be far freer from accountability. The Apostle says, “Everything is legitimate for me; not everything is expedient.” If everything is legitimate, that obviously includes self-discipline.
His approach then - apparently - is to justify ascetic behavior by starting with the so-called licentious heretics. In fact he has just dealt with the 'licentious' heretics in the previous section - the Valentinians, Basilideans and Carpocratians - and is proceeding to deal with the ascetic groups in what follows.
He starts off with a mention of Valentinians and then proceeds to a long citation of Basilides's son Isidore:
“So, if you have a quarrelsome wife” (I am quoting Isidore’s Ethics), “be patient with her, to avoid being wrenched violently out of God’s grace; get rid of the fire with your semen; then go to prayer with a good conscience.” 4 (3) “When your prayer of gratitude,” he goes on, “sinks to a petition, and your petition is that in future you may not act wrongly, rather than that you may act rightly – get married. (4) A man may be young or poor or highly sexed and unwilling to follow the Apostle’s advice and get married. He must not be cut off from his Christian brother. He should say, ‘I have entered the temple; there is nothing I can suffer.’ (5) If he has an inkling of what is happening to him, he should say, ‘Brother, lend me a hand to save me from going wrong.’ Then he will receive help, spiritually and physically. He has only to desire to achieve 5 the good, and he will attain it.
3(1) “But sometimes we say with our lips, ‘We do not want to sin,’ but our intention is disposed towards sin. Such a person refrains from doing what he wants to do out of fear of punishment being set to his account. (2) The human condition involves some things which are natural and necessary, others which are merely natural. 6 To wear clothes is natural and necessary; all this business of sexual intercourse is natural but not necessary.” 7
And then explains the quote as follows:
(3) I have passed on these statements to expose those followers of Basilides who do not lead upright lives, claiming that they have the authority actually to commit sin because of their perfection, or that they will in any event be saved by nature, even if they do sin, because of their ingrained election; their predecessors in the sect do not allow anyone to do the same 8 as they are doing. (4) So they should not wear the name of Christ as a cloak, live more licentiously than the most intemperate of the pagans, and bring ill-repute upon the name. [The Scripture text is] “Such men are false apostles, crooked workers” down to “whose doom shall match their acts.” 9 4(1) Self-discipline means disdain of the body, following obedience 10 to God. Self-discipline applies, not just to sexual matters, but to everything else for which the soul lusts improperly, because it is not satisfied with the bare necessities. (2) Self-discipline applies to speech, possessions and their use, desire generally. 11 It is not just that it teaches us self-control. It offers us the gift of self-control, a divine power and grace of God. 12 (3) I must tell you our people’s view of the matter. We bless abstention from sexual intercourse and those to whom it comes as a gift of God. We admire monogamy and respect for one marriage and one only. We say that we ought to share in suffering and “bear one another’s burdens,” 13 for fear that anyone who thinks he is standing firmly should in fact fall. 14 It is about second marriages that the Apostle says, “If you are on fire, get married.” 15
The point made here is very important because it serves as a lead in for his discussion of the Carpocratians in the chapter which follows (and which is in turn followed by the first reference to the Secret Gospel of Mark/Gospel according to the Egyptians. His point is that every heretic agrees that sex is sin, that childbirth is evil, but that the approach of the licentious and the ascetic heretics - the two divisions he mentions in chapter 5 - is different.
The licentious sects acknowledge what the Gospel of the Egyptians says about the evil of childbirth - at least implicitly - only they say that we are capable of sinning because we are perfect. The same is true with the Carpocratians who follow:
The followers of Carpocrates and Epiphanes think that wives should be held in common. 16 It is through them that the greatest ill-repute has accrued to the name of Christ.
Οἱ δὲ ἀπὸ Καρποκράτους καὶ Ἐπιφάνους ἀναγόμενοι κοινὰς εἶναι τὰς γυναῖκας ἀξιοῦσιν, ἐξ ὧν ἡ μεγίστη κατὰ τοῦ ὀνόματος ἐρρύη βλασφημία. [3.2.5.2]
Clearly the first line is acknowledging that Clement is thinking of the report in Hegesippus which we know from Lawlor is preserved word for word in Epiphanius (and to some degree in Irenaeus). But the highlighted words make absolutely clear that Clement's information about the sect comes from Hegesippus (which explains why Origen is like - I've never actually met a Carpocratian). First Epiphanius:
But they have been prepared by Satan and put forward as a reproach and stumbling-block for God's church. For they have adopted the name of 'Christian,' though Satan has arranged this so thatthe heathen will be scandalized by them and reject the benefit of God's holy church and its real message, because of their wickedness and their intolerable evil deeds— or, again, seeing the things they practise, may speak evil of us all, who have in fact no fellowship with them, either in doctrine or in morals, or in our daily conduct. But they lead a licentious life, and, to conceal their impious doctrines, they abuse the name, as a means of hiding their wickedness But in the words of scripture, 'Their damnation is just,' as the holy apostle Paul said. Because of their evil deeds the due return will be awarded them.
Irenaeus (only the highlighted line above is different)
These men, even as the Gentiles, have been sent forth by Satan to bring dishonour upon the Church, so that, in one way or another, men hearing the things which they speak, and imagining that we all are such as they, may turn away their ears from the preaching of the truth; or, again, seeing the things they practise, may speak evil of us all, who have in fact no fellowship with them, either in doctrine or in morals, or in our daily conduct. But they lead a licentious life, and, to conceal their impious doctrines, they abuse the name [of Christ], as a means of hiding their wickedness; so that their condemnation is just, Romans 3:8 when they receive from God a recompense suited to their works. (Irenaeus)
And then a lengthy citation of a work by Epiphanes whom he presumes to be a Carpocratian (which may or may not be the case given the number of errors in the section). And the concluding paragraph:
These are the doctrines of our noble Carpocratians. They say that these people and some other zealots for the same vicious practices gather for dinner (I could never call their congregation a Christian love-feast), men and women together, and after they have stuffed themselves (“The Cyprian goddess is there when you are full,” they say. 38), they knock over the lamps, put out the light that would expose their fornicating righteousness,” and couple as they will with any woman they fancy. 39 So in this love-feast they practice commonality. Then by daylight they demand any woman they want in obedience – it would be wrong to say to the Law of God – to the law of Carpocrates. I guess that is the sort of legislation Carpocrates must have established for the copulation of dogs, pigs, and goats. (2) I fancy he has, in fact, misunderstood Plato’s dictum in the Republic that wives are to be held in common by everyone. Plato really meant that before marriage they are to be available to any who intend to ask them to marry, just as the theatre is open to all spectators; but that once a woman has married she belongs to the particular man who secured her first and is no longer held in common by everyone. 40 11(1) Xanthus in his book entitled the Works of the Magi says, “The Magi think 4l it right to have sexual union with their mothers, daughters and sisters. The women are held in common by mutual agreement, not forcibly or secretively, when one man wants to marry another’s wife.” 42 (2) I fancy Jude was speaking prophetically of these and similar sects in his letter when he wrote: “So too with these people caught up in their dreams” who do not set upon the truth with their eyes fully open, down to “pompous phrases pour from their mouth.”
The idea then is quite clearly that the Carpocratian section is really filled with a lot of speculation. He has basically sandwiched (a) the original report about the Carpocratians in Hegesippus and (b) a Christian work by Epiphanes whom he presumes to have a Carpocratian provenance and (c) the oft repeated report about Christian love feasts. I think this connection between the Carpocratians and lovefeasts is found elsewhere in Clement. The point is that it derives from a deliberate pattern of obscuring that can also be connected with To Theodore.
In other words, Hegesippus obviously circulated widely. In that text there is the mention of a Marcellina who is identified as a Carpocratian (in Celsus's source a Harpocratian apparently). And this widely known report leads Clement to connect Epiphanes - who advocates Platonic shared women - to Carpocrates and the Christian practice of sexual licentiousness. I am not sure that this is what Epiphanes original meant. But I think this is the pattern which fits back to To Theodore. Theodore hears a report about a 'secret gospel' according to Mark which has 'naked with naked.' Clement disputes this characterization of the Alexandrian (Egyptian) gospel and cites the passage in question to disprove this evil interpretation. The connection with the Carpocratians follows a pattern of 'convenient lie' which extends to the Stromata.
“Finally, from so little sleeping and so much reading, his brain dried up and he went completely out of his mind.”
― Miguel de Cervantes Saavedra, Don Quixote