What is the context?
This verse belongs to 13:9–16. The writer contrasts strength through grace with reliance on food observances, then speaks of the altar and the earlier tabernacle service.
The next verses explain the connection through sin offerings whose blood entered the sanctuary and whose bodies were burned outside the camp. Jesus likewise suffered outside the gate. The contrast concerns participation in His sacrifice, rather than a claim that a Christian object can replace the need for Him.
The comparison concerns the specific offerings described in Leviticus 6:30 and 16:27. It should not be expanded into a claim that priests never ate any sin offering; Leviticus 6:26–29 describes offerings they did eat.
How is this passage commonly understood?
Calvin, Wesley and the USCCB note understand the altar in relation to Christ’s sacrifice, with Wesley naming the cross directly. The USCCB note does not identify the verse with the Eucharist. In these readings, the contrast directs people to the benefits of Christ’s offering rather than reliance on the earlier sanctuary service.
Where does this fit in God's plan?
Hebrews 10:10–18 explains why Christ’s one offering does not need to be supplemented by another offering for sin. That is the wider setting for what believers have in Him.
1 Peter 2:4–5 then describes the spiritual sacrifices offered by God’s people through Jesus. Hebrews itself names praise, generosity and doing good in 13:15–16. God’s purpose brings a people into grateful service through the sacrifice Christ has already made.
What is our position?
We don't have a position on this passage yet. When our study reaches a conclusion the text supports, it will appear here.