Do Protestants think of Mary as the "Mother of All Peoples"?

The word Protestant covers a lot of ground and some dispute as to who belongs to that group or not.

Early Protestant Reformers were originally Catholics and mostly continued believing much of Catholicism’s Mariology, though that generally changed over the years, provided they were not killed and actually had time to review all their inherited beliefs.

Most of those reformers were vastly different in their beliefs from beginning to end. The churches or religions which sprang from them however have stagnated, sometimes not even following their founders final or later theology.

Most Protestant faiths now recognise Mary as a fallible human like everyone else and ascribe no special place or dogma regarding her at all.

A slightly concise but reasonably useful writeup can be found in “Protestant views on Mary” at Wikipedia. https://en.m.wikipedia.org/wiki/Protestant_views_on_Mary

The simple answer from mainstream Protestantism (if such a term is possible) is no. It is only when Mary approaches the status of the second Eve, in much the same way that Christ is the second Adam, that this theological tendency arises. Since mainstream Protestantism strives towards 'Sola Scriptura' and since Mary as the second Eve cannot be found in Scripture without much theological gymnastics, the answer is no.

A corollary of this is to say that, as Eve disobeyed in the garden and Adam cooperated with her, so Mary obeyed and undid Eve's wrong just like Christ undid Adam's wrong. The problem is that this makes Mary's obedience primary since Mary's obedience brought forth the Christ so that he could obey.

Paul clears this up by declaring that the woman was deceived but Adam was not. He neither cooperated with Eve nor was he tricked by her. He received the command from God before Eve's creation and he alone transgressed. Eve became a transgressor because she was 'of Adam'...In Adam all die (1 Cor. 15:22).

"This at last is bone of my bones and flesh of my flesh; she shall be called Woman, because she was taken out of Man." - Genesis 2:23

Mary as the second Eve has nothing she can correct, it is Adam who must be redeemed.

I am quoting, below, from the Second Helvetic Confession which is a generally accepted statement of the Reformation :

It was adopted by the Reformed Church not only throughout Switzerland but in Scotland (1566), Hungary (1567), France (1571), Poland (1578), and after the Westminster Confession of Faith, the Scots Confession and the Heidelberg Catechism is the most generally recognized confession of the Reformed Church. The Second Helvetic Confession was also included in the United Presbyterian Church in the U.S.A.'s Book of Confessions, in 1967, and remains in the Book of Confessions adopted by the Presbyterian Church (U.S.A.).

Helvetic Confessions - Wikipedia

The Helvetic Confession only makes one mention of Mary, the mother of Jesus :

For Scripture has delivered to us a manifest distinction of persons, the angel saying, among other things, to the Blessed Virgin, "The Holy Spirit will come upon you, and the power of the Most High will overshadow you; therefore the child to be born will be called holy, the Son of God" (Luke 1:35)

Chapter III - The Second Helvetic Confession

In regard to images in general there is this statement :

But in fact in order to instruct men in religion and to remind them of divine things and of their salvation, the Lord commanded the preaching of the Gospel (Mark 16:15) - not to paint and to teach the laity by means of pictures. Moreover, he instituted sacraments, but nowhere did he set up images.

Chapter IV - The Second Helvetic Confession

As noted in comment, above, the only place in scripture to speak of a woman being a 'mother' to all humanity is the pronouncement upon Eve when Adam named her :

And Adam called his wife's name Eve; because she was the mother of all living.

[Genesis 3:20, KJV]

As noted in comment, the Wikipedia entry on Anglican Marian Theology does not carry sufficient citation to be a reliable statement of the very broad spectrum of belief within the Anglican/Anglo-Catholic community.