Animal sacrifices stopped having any meaning to God after the cross. They are a work of unbelief. Men have done and do lots of worthless things, and animal sacrifice is one of them.
I don't necessarily believe that the abomination that makes desolate is one thing. The one in the LXX version of Daniel 9:27 is obviously about Christ and what could be more abominable than the murder of the son of God? It's possibly like the day of the lord in prophecy in which there have been more than one.
And one week [he] shall establish the covenant with many: and in the midst of the week my sacrifice and drink-offering shall be taken away: and on the temple [shall be] the abomination of desolations; and at the end of time an end shall be put to the desolation. Daniel 9:27