Albert Barnes on Hebrews 13:10

We have an altar. We who are Christians. The Jews had an altar on which their sacrifices were offered which was regarded as sacred, and of the benefit of which no others might partake. The design of the apostle is to show that the same thing substantially, so far as privilege and sanctifying influence were concerned, was enjoyed by Christians. The "altar" to which he here refers is evidently the cross on which the great sacrifice was made.

Whereof they have no right to eat which serve the tabernacle. A part of the meat offered in sacrifice among the Jews became the property of the priests and Levites, and they had, by the law, a right to this, as a part of their support. See Lev 6:25,26, Nu 18:9,10. But the apostle says that there is a higher and more valuable sacrifice of which they have no right to partake while they remain in the service of the "tabernacle" or temple; that is, while they remain Jews. The participation in the great Christian sacrifice appertained only to those who were the friends of the Redeemer; sad however much they might value themselves on the privilege of partaking of the sacrifices offered under the Jewish law, that of partaking of the great sacrifice made by the Son of God was much greater.

Which serve the tabernacle. Heb 9:2,3. The Jewish priests and Levites.