Do Protestants accept the similarity between Mary and the Ark of the Covenant? Catholics believe that Mary is the Ark New Testament and they believe it on a scriptural basis (source).This is the same stance Orthodoxy has (source).



Do Protestants accept the similarity between Mary and the Ark of the Covenant?

If yes,  then, that would mean agreeing with Catholic (and Orthodox) interpretation.

If not, why not?



The following are the similarities between Mary and the Ark of the Covenant as seen in light of Biblical typology (Catholic Interpretation):

The Ark


The Ark of the Covenant was overshadowed (Ex. 40:34-35)
David was rejoicing in the presence of the Ark of the Covenant (2 Sam. 6:16)
David said, Why did the Ark of the Lord visit me? (2 Sam. 6:9)


Mary


Mary was overshadowed by the Holy Spirit (Lk. 1:35)
John the Baptist leaped for joy in the presence of Mary (Lk. 1:41)
Elizabeth said, Why did the mother of the Lord visit me?( Lk. 1:43)


Also, the Greek word ἐπισκιάσει was the same Greek word used in the overshadowing of the Ark ( Exodus 40:35 LXX).In the entire Scriptures, only Mary and the Ark were ascribed of that verb.



Protestants of different denominations are encourage to answer.
If you look hard enough you can always find similarities. The correspondences between Mary and the Ark of the Covenant remind me a lot of Islamic arguments that Muhammad was the prophet Moses prophesied about in Deuteronomy 18:18-22 rather than Jesus.

According to Muslim apologists, there are many similarities between Moses and Muhammad, many of which do not apply to Jesus (source: whyislam.org):


both were prophets
both had normal human parents
both had wives and children
both had normal deaths
both had spiritual and legal missions, and both served as both a prophet and governor
both were generally accepted as leaders by their people, unlike Jesus
both waged war


But according to Christian apologists, most of these miss the point. While they may be true, the important characteristics of Moses were not that he had a wife and children. Instead the similarities we should be looking for are things like this (source: answering-islam.org):


Moses performed miraculous signs
Moses spoke directly with God
Moses was assured of his calling by God directly, rather than by his wife
Moses's revelations did not need to be abrogated by himself
And unlike Muhammad, Moses never thought he was demon possessed, never became delirious, and never spoke words of Satan (and the link above contains other disturbing claims)


For most Protestants the points of similarity given in the question between the Ark and Mary would look like you're grasping at straws. The similarities are real, but unimportant. The important things about the Ark of the Covenant are the following:


On the day of Atonement the High Priest would take the blood of the bull and goat (which were sacrificed as sin offerings), and sprinkle it over the Ark, making atonement for the nation. This soteriological role points only to Jesus. Some Catholics call Mary Co-Redemptrix, but that is not even official Catholic Dogma!
The cloud of God's presence was positioned above the Ark, demonstrating that God dwelled within his people. But they were cut off from him, behind a curtain only one man could pass through once a year, outside a temple restricted to the priests, behind a system of expensive and bloody sacrifices.
Mary bore Jesus the Son of God, who came to dwell among his people (John 1:14). God's presence at the Ark is a tiny shadow of his presence in the person of his Son, but as such the Ark is pointing to Jesus, not Mary. I don't think the Ark could really be considered to have ever carried God, rather it was the location where God descended to be with his people. If anything, the way in which Mary led to God dwelling with his people is far beyond what the Ark did, and comparing her with the Ark is a negative comparison.
God was holy and so the Ark was holy. But almost all protestants reject the idea of Mary's immaculate conception believing instead that she is a sinner like the rest of us. There is no comparison between the Ark's holiness and hers. Mary's righteousness is imputed to her through her faith in the gospel, not because she carried the embryonic Jesus.