I can see why it would be outdated, don't see why any part of the law would be repugnant. After all, Paul says that the Law is holy; and Jesus said not one jot or tittle would fail. Those are 2 pretty powerful statements of support.
I see no reason for it to be an affront. I'm sure Jesus is aware that His was the only effectual sacrifice, and that the others were signs of the better that was to come. Likewise, I doubt He'll find bread and wine repugnant or an affront in some future dispensation.
Judaizing
The Judaizers were castigated for suggesting to Gentiles that salvation required cutting one's flesh. As Jews, they were perfectly free to engage in temple ritual. In fact, Paul and friends did so in Acts 21.
It’s quite simple.
“But we know that the law is good if one uses it lawfully,” (1 Tim. 1:8)
The OT law had it place prior to the coming of Christ. It was lawful to offer animal sacrifices in the manner stipulated by God.
Once Christ came and made the final, once for all time sacrifice for sin, that OT command no longer had any lawful use. That is the plain testimony of Hebrews, Galatians, etc in the NT.
So to suggest that in the future, after the coming of Christ to atone for the sins of His people, that such OT sacrifices would again be made, is repugnant and an affront to the Lord Jesus Christ.
Dispensational confusion comes about by failing to see the distinction between the OT sacrifices and the new covenant sacraments of baptism and the Lord’s Supper, which were specifically given by our Lord to the Church to be done often until He comes again.