How do devout Jews sacrifice today?

Every unbelieving Jew remains under the Old Covenant and the Law it contains, including the requirement to observe the rites and sacrifices in the temple. Obviously, this requirement poses a serious dilemma for any Jew who wishes to remain orthodox and obedient to the Law. WIthout a temple, the Jewish people are prevented from observing the sacrifices as required by the Law. Therefore, they are forced to live in a constant state of disobedience to the Old Covenant.

This situation has persisted since the destruction of the temple in AD 70, and there is no solution for their problem except to have faith in Messiah and come out from under the Law. Therefore they live in a perpetual state of frustration and concern over their plight. Perhaps a pious Jew finds some consolation in knowing their disobedience is involuntary, having been prevented from obeying by circumstances beyond their control.

Still, this situation was exactly what the Lord intended when He called for the destruction of the temple in Matthew 24:

Luke 21:20  “But when you see Jerusalem  surrounded by armies, then  recognize that her desolation is near.
Luke 21:21 “Then those who are in Judea must flee to the mountains, and those who are in the midst of  the city must leave, and  those who are in the country must not enter  the city;
Luke 21:22  because these are  days of vengeance, so that all things which are written will be fulfilled.
Luke 21:23  “Woe to those who are pregnant and to those who are nursing babies in those days; for  there will be great distress upon the  land and wrath to this people;
Luke 21:24  and they will fall by  the edge of the sword, and will be led captive into all the nations; and  Jerusalem will be  trampled under foot by the Gentiles until  the times of the Gentiles are fulfilled.
 

The destruction of the temple and the elimination of any opportunity to participate in the sacrificial system was a situation the Lord Himself instituted to send a message regarding the Old Covenant. As the writer of Hebrews taught:

Heb. 8:13  When He said, “A new covenant,” He has made the first obsolete. But whatever is becoming obsolete and growing old is ready to disappear.
 

Heb. 9:8  The Holy Spirit is signifying this, that the way into the holy place has not yet been disclosed while the outer tabernacle is still standing,
Heb. 9:9 which is a symbol for the present time.
 

The Old Covenant earned its name because a new and better covenant was intended to replace it. The OT Law established the existence of the temple, and so for as long as the temple existed, the writer says, it was an indication to saints that the new had not yet come. But once the new covenant had been given, the Old Covenant and the temple it established were eliminated to show that they were no longer needed.

Therefore, the Lord worked through the Romans to destroy the temple after Christ's arrival. He does not want the Jew to continue seeking the Lord in a temple and through a Law that was fulfilled in Christ and no longer needed. Their collective frustration in trying to observe a Law absent a temple is part of God's plan to frustrate the nation of Israel during this time of hardening, as Paul wrote:

Rom. 11:7  What then? What Israel is seeking, it has not obtained, but those who were chosen obtained it, and the rest were hardened;

Rom. 11:11  I say then, they did not stumble so as to fall, did they? May it never be! But by their transgression salvation has come to the Gentiles, to make them jealous.
 

Scripture quotations taken from the (NASB®) New American Standard Bible®, Copyright © 1995, 2020 by The Lockman Foundation. Used by permission. All rights reserved. www.lockman.org