In Acts 6:7 we find that a large number of Israel's cohens (priests) became obedient to the Messianic faith. But in Hebrews 13:10 is the rather cryptic statement that none of the cohens who were ministering in the Temple at the time of the writing of Hebrews had any right to eat from the heavenly alter, to which every true follower of Yeshua has unlimited access. I take it from that comment that all of the cohens who belonged to Yeshua had been "drummed out" of service in the Jerusalem Temple by that time. In fact, the formal exclusion of all the Messianics from Temple service may well have been the immediate occasion for Rav Sha'ul's writing this epistle. Whether I'm right about that or not, the Book of Hebrews was clearly written in the context of some serious act of discrimination against Messianics by the mainstream Jewish Community.
The comfort Rav Sha'ul gives to these wounded Messianics, confused by their rejection in God's own Covenant Community, written perhaps in time for their first Yom Kippur excluded from the Temple (Remember how it felt the first Yom Kippur you had no synagogue to go to, because of your following Yeshua?), is to point them upward to the Heavenly Temple service, where Yeshua is our eternal Cohen Hagadol and sacrifice, where Messiah perfectly fulfills the Torah's Yom Kippur symbolism for us today, and where the earthly pictures become more-or-less irrelevant in the light of the divine realities. Then he says, in effect, "Pay more careful attention to your own spiritual condition at this vulnerable time of your walk with the Lord, and encourage and help each other every day." That's not bad advice for us now, either: Hebrews 3:12-13, "Take care, brothers and sisters, that there not be in any one of you an evil, unbelieving heart that falls away from the living God. And encourage one another every day, as long as it is called 'today,' so that none of you will be hardened by the deceitfulness of sin."
Rav Sha'ul lets us know that God's new work is better than His earlier work, more spiritual, more eternal, heavenly rather than earthly, soon to culminate in the salvation of all Israel. He is careful not to criticize Israel's current leadership or worship, as instituted by God in His eternal, heavenly Torah, even going so far as to not mention his own name, and to keep himself in the background. (Contrast that with his other letters, such as II Corinthians, where he is arguing against ignorant heretics with no legitimacy.) But he makes his point clear, that, good as the earthly symbolism is, we can do without it if we need to, because we have the better and greater, the ultimate Reality.
These ideas should not have been new to his readers. Indeed, he criticizes them for having lost sight of the truth he is presenting. (Hebrews 5:11-6:12). For example, it was commonplace in ancient middle eastern thought to consider an earthly Temple to be a physical replica of heavenly, spiritual, realities, to consider the earthly Mount Zion (or Zaphon or Olympus, depending on one's religion) to be a model of the heavenly one, as well as the foundation-stone of the present cosmos. But it is easy for us all, in difficult times, to loose sight of the truth we know, the truth we need to return to:
May He give us all a clearer vision.