Where he condemns those who do not discern His body, 1 Cor. 11:29. Also see 1 Cor. 10:16, the entire discourse there is about different understanding of the altar sacrifice:
16 The chalice of benediction, which we bless, is it not the communion of the blood of Christ? And the bread, which we break, is it not the partaking of the body of the Lord? 17 For we, being many, are one bread, one body, all that partake of one bread. 18 Behold Israel according to the flesh: are not they, that eat of the sacrifices, partakers of the altar? 19 What then? Do I say, that what is offered in sacrifice to idols, is any thing? Or, that the idol is any thing? 20 But the things which the heathens sacrifice, they sacrifice to devils, and not to God.
Note that he doesn't say "Israel eats of the sacrifices and we don't"; he compares the two sacrifices and says that one precludes another.
That the Eucharist is an act of thanksgiving is Catholic teaching: we come to thank Christ for His sacrifice. If no sacrifice were occurring at Mass, we could just as well do the thanking at home.
He is not teaching that Jesus is being offered in sacrifice. He is teaching about not associating with idolaters via eating food sacrificed to idols. In similar manner, we are identified as followers of Christ via Eucharist.
So just as taking Eucharist identifies us as Christians, eating food sacrificed to idols identifies them with demons.
Mega bad idea.
From Barnes, who ties it all together in a context spanning multiple chapters:
(3.) Whether, when invited to the houses of the heathens, they might partake of the meat sacrificed to idols, and which was set before them as a common meal. I regard this chapter as having a very close connexion with \\1Co 8\\. In the close of chapter 8, (1 Corinthians 9:13,) Paul had stated, when examining the question whether it was right to eat meat offered in sacrifice to idols, that the grand principle on which he acted, and on which they should act, was that of self-denial. To illustrate this he employs the ninth chapter, by showing how he acted on it in reference to a maintenance; showing that it was this principle that led him to decline a support to which he was really entitled. Having illustrated that, he returns in this chapter to the subject which he was discussing in chapter 8; and the design of this chapter is further to explain and enforce the sentiments advanced there, and to settle some other inquiries pertaining to the same general subject. The first point, therefore, on which he insists is, the danger of relapsing into idolatry—a danger which would arise, should they be in the habit of frequenting the temples of idols, and of partaking of the meats offered in sacrifice, 1 Corinthians 10:1-24. Against this he had cautioned them in general, in 1 Corinthians 8:7,9-12. This danger he now sets forth by a variety of illustrations. He first shows them that the Jews had been highly favoured, had been solemnly consecrated to Moses and to God, and had been under the Divine protection and guidance, (1 Corinthians 10:1-4;) yet that this had not kept them from the displeasure of God when they sinned, 1 Corinthians 10:5. He shows that, notwithstanding their privileges, they had indulged in inordinate desires, 1 Corinthians 10:6; that they had become idolaters, 1 Corinthians 10:7; that they had been guilty of licentiousness, 1 Corinthians 10:8; that they had tempted their leader and guide, 1 Corinthians 10:9; that they had murmured, 1 Corinthians 10:10; and that, as a consequence of this, many of them had been destroyed. In view of all this, Paul cautions the Corinthians not to be self-confident, or to feel secure; and not to throw themselves in the way of temptation by partaking of the feasts of idolatry, 1 Corinthians 10:12-14. This danger he further illustrates (1 Corinthians 10:15-24) by showing that if they partook of those sacrifices, they in fact became identified with the worshippers of idols. This he proved by showing that in the Christian communion, those who partook of the Lord’s Supper were identified with Christians, 1 Corinthians 10:16,17; that in the Jewish sacrifices the same thing occurred, and those who partook of them were regarded as Jews, and as worshippers of the same God with them, 1 Corinthians 10:18; and that the same thing must occur, in the nature of the case, by partaking of the sacrifices offered to idols. They were really partaking of that which had been offered to devils; and against any such participation Paul would solemnly admonish them, 1 Corinthians 10:19-22. Going on the supposition, therefore, that there was nothing wrong in itself in partaking of the meat that had been thus killed in sacrifice, yet Paul says (1 Corinthians 10:23) that it was not expedient thus to expose themselves to danger; and that the grand principle should be to seek the comfort and edification of others, 1 Corinthians 10:24. Paul thus strongly and decisively admonishes them not to enter the temples of idols to partake of those feasts; not to unite with idolaters in their celebration; not to endanger their piety by these temptations.
There were, however, two other questions on the subject which it was important to decide, and which had probably been submitted to him in the letter which they had sent for counsel and advice. The first was, whether it was right to purchase and eat the meat which had been sacrificed, and which was exposed indiscriminately with other meat in the market, 1 Corinthians 10:25. To this Paul replies, that as no evil could result from this, as it could not be alleged that they purchased it as meat sacrificed to idols, and as all that the earth contained belonged to the Lord, it was not wrong to purchase and to use it. Yet if even this was pointed out to them as having been sacrificed to idols, he then cautioned them to abstain from it, 1 Corinthians 10:28. The other question was, whether it was right for them to accept the invitation of a heathen, and to partake of meat then that had been offered in sacrifice, 1 Corinthians 10:27. To this a similar answer was returned. The general principle was, that no questions were to be asked in regard to what was set before them; but if the food was expressly pointed out as having been offered in sacrifice, then to partake of it would be regarded as a public recognition of the idol, 1 Corinthians 10:28-30. Paul then concludes the discussion by stating the noble rule that is to guide in all this: that everything is to be done to the glory of God, 1 Corinthians 10:31; and that the great effort of the Christian should be so to act in all things as to honour his religion, as not to lead others into sin, 1 Corinthians 10:32,33.