We have an altar, whereof they have no right to eat which serve the tabernacle.
Christianity and Judaism are so totally distinct that 'they who serve the (Jewish) tabernacle' have no right to eat our spiritual meat-namely, the Jewish priests, and those who follow their guidance in serving ceremonial ordinance. He says, "serve the tabernacle;" not 'serve IN' it: servile worship. Contrast Philippians 3:3. An altar - Christ's cross, whereon His body was offered. The Lord's table represents the cross, as the bread and wine represent the sacrifice offered on it. Our meat which we by faith spiritually eat is the flesh of Christ, in contrast to typical "meats." The two cannot be combined (Galatians 5:2). Dr. Waldegrave explains the "altar," Christ's Godhead, on which He offered His manhood; because:
(1) "The altar ... sanctifieth the gift" (Matthew 23:19);
(2) Prevents the sacrifice being consumed, as the manhood would have been by God's judicial wrath but for the Godhead.
Neither holds good of the cross, contact with which involved a curse. Rather, Christ, at once the Altar, the Sacrifice, and the Priest. "We have" Him by faith: so need no further sacrifice or sacrificial "meats" (note, Revelation 6:9). That not a literal eating of the sacrifice of Christ is meant in the Lord's supper, but a spiritual, appears from comparing Hebrews 13:9 with Hebrews 13:10, "with GRACE, NOT with MEATS." As the sacerdotal priest's duty was to 'wait at the altar,' so the Christian minister's is to "preach the Gospel" (1 Corinthians 9:13-14).