It's helpful to remember that the book of Acts is an historical account, and not primarily a book from which to derive doctrine. Simply put, it's an account of what actually happened, not necessarily what should have happened in the fledgling Body of Christ.
The Temple was still standing, God giving Israel a generation (about 40 years between the Crucifixion and the destruction of the Temple) to transition from the Old Covenant to the New Covenant. The letter to the Hebrews was a clarification of the Old Covenant inferiority in the light of the Reality of Christ and the vastly superior New Covenant established in His Blood, Resurrection, Ascension, and Perfect, Permanent High Priesthood. "What is old and is passing away . . . " refers to the eventual destruction of the center of Old Covenant practices - which still stood at the time of its writing - the Temple and the Levitical priesthood. God allowed for a poignant end to the Old covenantal system, and established the New permanently, with a permanent High Priest from the Tribe of Judah authorized by an oath from God and by the power of an indestructible Life (see Hebrews 7-10).
I believe Paul's action was in response to pressure from those in authority in the Body in Jerusalem - he was deferring to their concerns to avoid offense. His statements elsewhere about being all things to all people in order to win some could apply here, though this would have been a good place to take a stand for the finished Work of Christ. Again, Acts is not a collection of perfect actions held up as an example, but an account of the very earliest days of the acts of the Apostles and of the effects of the Gospel of Grace.
Also of note is that Paul never actually participated in the offering of sacrifices. He was arrested instead. Providential intervention? Perhaps.
It is clear from the letters from which we ARE to learn doctrine that Christ was the Perfect, Final Sacrifice, once for all and that the Body did not participate in sacrifices.
Sacrifices in the Millennium (if it's a literal time period at all)? No way! Jesus is our Perfect, Permanent High Priest, from the tribe of Judah. For Him to administrate such practices would be illegal.
Sacrifices in a Tribulation period (again, if such a period of time is literal)? Probably - but they won't be initiated by God, for Christ was the Final and Perfect Sacrifice once for all. Such practices would be an abomination. If sacrifices happen in a literal Tribulation period, they will be both initiated and stopped by an anti-Christ spirit - illegal acts from a false authority working to deceive.
As Bookends stated earlier, unrevealed prophecy must be measured by revealed Truths.
Consider the following:
- Who Christ is
- What He came to do
- What that actually accomplished, and
- Who believers are in Him
When one has a grasp on those truths, falsehoods tend to fall away, like the silly notion that believers will be offering sacrifices at ANY time with Christ overseeing it all! It's unthinkable after a straight read-through of Hebrews 7-10!
Try not to get hung up on Paul's actions in Acts 21 - again, remember that it is more of a history than a template for doctrine.
-JGIG