"Do not be swept off your feet by various peculiar teachings. Spiritual stability depends on the grace of God, and not on rules of diet — which after all have not spiritually benefited those who have made a speciality of that kind of thing. We have an Altar from which those who still serve the tabernacle have no right to eat. When the blood of animals was presented as a sin-offering by the High Priest in the sanctuary, their bodies were burned outside the precincts of the camp. That is why Jesus, when he sanctified men by the shedding of his own blood, suffered and died outside the city gates. Let us go out to him, then, beyond the boundaries of the camp, proudly bearing his 'disgrace.'" Hebrews 13:9-13
Like so much of what we've seen throughout Hebrews, these few verses have hidden deep depths of goodness and richness for us to enjoy. There's also a kind of rhetorical elegance here. Have any of you ever heard the term "chiasmus" before? It's a figure of speech that turns in on itself in the arrangement A-B-B-A; the most famous example of which is probably JFK's, "Ask not what your country (A) can do for you (B), ask what you (B) can do for your country(A)." These kind of expressions stick with us because they tend to pull us in, and sort of enwrap us in their logic...
That's what happening here in Hebrews 13:9-13. As it now pertains to the priesthood of believers over against the old Hebraic systems of the priests:
"Grace is not to be found through our food and our location, it is by His food and His location that we are invited into His grace."
In the Old Covenant, the priests sought and maintained grace by the careful keeping of meal and meat offerings in the cloistered confines of holy sequestered spaces not open to the common man. In the New Covenant, by feasting upon Jesus, by going outside the religious camp, we encounter His grace, even while "sharing in his disgrace," and show His availability to everyone we meet.
That's why - all along - the writer of Hebrews has been saying, "Don't let the Way of Jesus get under its own systems" - because that had been Judaism and it was no longer the way. The engine of this thing is now the Holy Spirit and He is miles ahead of our best human-religious systems and plans. All this happens outside of safe churchly spaces and at the pace of the Spirit, not our pace. And may we never forget that!