Romans is crystal clear that (a) God only has one family, not two (or any other number), and (b) the believing Gentiles are grafted into that family in place of the unbelieving. Why is there really any argument over that?
No matter how it got there, the Church is now God’s people
One family, not two. God's people encompass both believing Jews and believing Gentiles. Read the New Testament.
and the beneficiary of the promises God made Israel in the Old Testament.
Certainly not! Those promises, from the Church's point of view, are typological. They point to bigger things. The real "land of milk and honey" is heaven, not a tract of land in the eastern Mediterranean. The real "exodus" is the believer's conversion from sin and death to life and faith in Christ. And so forth.
It doesn't follow that the original promises, to the original people to whom they were made, in the original sense in which they were understood, are any less valid. The gifts of God are without repentance.
Consequently, Jacob’s blood descendants have no unique destiny
It's settled Catholic doctrine that the conversion of the Jews is one of the events that herald the Second Coming. Obviously they have a unique destiny, or they wouldn't be here. (Ever met a Hittite? Me neither.)
and modern Israel’s existence has no significance.
I think we should be careful about equating "Israel" in Scripture with "Israel" on the (present-day) map. "Israel" in Scripture always included all twelve tribes. "Israel" on the map today doesn't, and probably can't.
Does modern-day "Israel" have prophetic significance? Maybe, watch and see.
Articles like these amount to elaborate strawman arguments, at least as far as Catholics are concerned. Maybe they are more meaningful against, e.g., dominionist Presbyterians. Maybe not, I don't know.
This article is addressed to you, but I wouldn’t expect you to understand it because your baseline is 180 degrees off and dictated by others who read the Bible for you.
Do you stand with Israel and Jews or not?
Are they not God’s Children?
If you answer ‘no’ to either - you’ve got problems.
Well, without even reading the long article, the conflict I see as regards the place of Israel whether the regathering of Jews today and establishment of the State of Israel is a fulfillment of prophecy, which replacement types reject, along with the further conversion of (what is left) of Israel. Rome has a history of being reluctant to support the establishment of the former (besides past anti-antisemitism, as with Luther also), while affirming the latter. (CCC 674).
Related to this is the rejection of the literal 1,000 reign of Christ, which is well-supported.