If our hearts are established with grace, "We have an altar, whereof they have no right to eat which serve the tabernacle" (Heb. 13:10). The altar here represents the place of acceptance with God and worship of God. If our hearts are established with grace, our altar is Christ Jesus. It is through Him, "the Beloved" (Eph. 1:6), based on the merits of His obedience and death, that we who believe are accepted with God and are enabled to worship God in spirit and in truth.
Those who "serve the Tabernacle" here are those who seek acceptance with God based on something other than the merits of Christ's blood and righteousness. They either totally reject Him, or they are ignorant of His righteousness, or they are not submitted to it in some way. How are we who believe to view these? We are to see them as condemned, lost, and as those whose deeds are evil, whose worship is totally unacceptable to God as it is the fruit of unbelief and self-righteousness. We cannot speak peace to them, and we cannot have religious fellowship with them. They have no "right," no liberty, power, authority, or privilege, to eat, to worship at our altar because they have rejected our Altar which is Christ.
In the Old Covenant the altar is what gave value to the sacrifice. Christ became incarnate and obeyed the law as our Representative. He offered the sacrifice of His humanity (body and soul) upon the altar of His Deity. It was His Deity (His Altar) that gave value to His sacrifice. It is not our faith, our repentance, nor our works that give value to Christ's work of redemption on the cross.