“not by foods through which those who were so occupied were not benefitted”
This is an obvious reference to Lev. 11. The food laws had passed away in Christ (cf. Matt. 15:11; Mark 7:18-23; Acts 10; Col. 2:16-23). They were no longer binding on believers for salvation, but in a church setting, believers were still to be conscious of “weaker brothers” (cf. Rom. 14:1-15:6; I Cor. 8: 10:23-33) and to try not to offend their weak consciences.
13:10 “We have an altar”
The analogy seems to be a spiritual (heavenly) tabernacle, not a physical altar and, therefore, it refers to Jesus’ sacrificial work on behalf of believers. It is a powerful metaphor of our access to God through Christ.