Actually, not, assuming objective truth.
If Jesus is the true Messiah, of both Jews and Gentiles, as Christianity from the New Testament on has always claimed, then those who trust in Jesus alone would be God's "chosen people" today... and Christianity would be the rightful heir to Old Testament Judaism... As weird as it sounds, modern Judaism, from this New Testament perspective, would be the 'heretical sect' of the ancient Judaism of the Temple and the Ark of the Covenant, since it has rejected the Messiah.
Yes there can be a place for the Jewish people in the future, but only through the Messiah, Jesus. This is standard traditional cross-denominational Christian theology.
Christians have always acknowleged the legitimacy of the religion of Old Testament Judaism, modern Judiasm though, because of its rejection of Jesus as Messiah, essentially recognizes no religious value at all to Christianity or its relics.
It would be well to remember modern Christianity, like ancient Judaism did, relies on BLOOD SACRIFICE for salvation, whearas modern Judaism (since they have no temple) does not ...hence Christianity in that one essential has more in common with ancient Judaism than modern Judiasm.
A lot of assumptions there. Just for sake of argument, let's say the Ark is unconvered in Antarctica, and looking at it doesn't kill you.
Where should it be displayed of the following three choices:
a) The Vatican
b) National Museum of Israel (or whatever it's called)
c) The Smithsonian Museum
Of course using that reasoning (which I agree with), the ark of the covenant would have no place in the life of the church. It is just a neat historical relic.