Hebrews 13:10

We have an altar. The writer here alludes to the fact that the priests and the Levites were assigned certain portions of some of the sacrificial animals brought to the ancient sanctuary or to the Temple (see Lev. 6:16-18; 7:15, 16, 31-34; Num. 18:8-10; Deut. 18:1, 2; cf. 1 Cor. 9:13). Perhaps the false doctrines referred to in Heb. 13:9 had stressed the importance of requiring Christians to practice the ancient rites and ceremonies of Judaism, which dealt with meats and drinks, as if a superior state of holiness could thereby be attained. But Christians have an altar, the cross of Calvary, and a sacrifice far surpassing the ancient animal sacrifices in value and efficacy (see on chs. 9:14, 24-28; 10:10, 12, 14). This was none other than “the Lamb of God, which taketh away the sin of the world” (John 1:29). Furthermore, Christ calls upon those who believe in Him to eat of His flesh (see John 6:33-58).

They ... which serve. That is, the priests and the Levites.

No right to eat. Within the orbit of the Jewish religious system the priests and Levites enjoyed an honored position and special privileges. But, having rejected Jesus, they were unworthy, in spite of their exalted position, to partake of that to which all true Christians have a right. Paul may also have been thinking of the bread and the wine of the Lord’s table. Under any circumstances, the vaunted merits of the system of religion referred to as “divers and strange doctrines” in v. 9 were infinitely inferior to the way of salvation through faith in Jesus Christ.