A lot of Christian doctrines are considered quite controversial in today's culture. No sex outside of marriage. Give away your possessions. Love your enemies. And the idea found in Hebrews 9 is also liable to rankle modern sensibilities. Forgiveness requires the shedding of blood? Why? Why can't God just forgive and call it good?
It may be tempting to lay our sin problems at the feet of God and angrily insist He do something about them. But to demand that God look the other way when it comes to the high cost of forgiveness and pretend that no serious (i.e. life-ending) consequences of sin exist, then we are asking for something that is neither just nor true nor in our best interests.
When modern Americans recoil at the blood requirement for forgiveness, the problem is that we are focusing on the difficulty and expense of the solution rather than appreciating the evil nature of sin. We are guilty not only of our sins - but also of underestimating the spiritual damage that they wreak in our relationship with God. The Bible never downplays sin, and neither should we.
Besides all this, it is of utmost importance to remember that God did indeed "do something" about our sin problems. However, He didn't excuse them or look the other way. He knew that a high price of blood had to be paid for the sins of the world. Yet here's the thing - the debt was paid. Christ's blood was shed. Our forgiveness was indeed achieved, but it wasn't our blood that was required in the end. Christ did it for us, on our behalf.
We may recoil at the action that was needed, but our hearts should sing at the glory of His grace!