Non-Jewish Christians are so accustomed to reading Hebrews 7-10 as something close to anti-Jewish. “At least since the time of John Chrysostom, Hebrews has been read as a stern warning to Jewish converts to the Christian faith not to fall back into Jewish practices” (R. Hays).
It’s important to keep in mind, however, that if the specific situation faced by this community had not emerged, the letter “to the Hebrews” would not have been necessary. The writer would not have made these sorts of arguments in chapters 7-10.
We only have this letter because a crisis has driven the hearers to a point where they must choose between their identity as Christians and their identity as Jews. Apart from that situation, however, there would be no inherent tension between being faithfully Jewish and thoroughly Christian.
That may be a ridiculous understatement to Christian Jews (it certainly would be to the early church), but for many non-Jewish Christians, shaped as we are by a longstanding divide between Judaism and Christianity, it’s difficult to wrap our minds around.