'Participate' in the Bible

Do you not know that the unrighteous will not inherit or have any share in the kingdom of God? Do not be deceived; neither the sexually immoral, nor idolaters, nor adulterers, nor effeminate [by perversion], nor those who participate in homosexuality,

Is the cup of blessing which we bless [at the Lord’s Supper] not a sharing in the blood of Christ? [Indeed it is.] Is the bread which we break not a sharing in the body of Christ? [Indeed it is.]

Consider Israel according to the flesh. Don't those who eat the sacrifices participate in the altar?