From my protestant experience the focus is solely on how Mary herself is regarded. Really in my experience it's "Queen of Heaven" that gets challenged more than "Mother of God". But both together seem to suggest that Mary is regarded as some sort of goddess to the average protestant. Most don't know about Nestorius and Chalcedonian etc. They just see statues of Mary everywhere and people praying to them. So many Catholic Churches being named after Mary. Mary seems quite dominant in Catholicism.
Which demonstrates that what many Protestants are dealing with is their own phobia of Rome. There are degrees of this phobia that we see in parts of the Protestant and post-Protestant (a term I'm using to describe various modern sects such as the Jehovahs's Witnesses and other non-orthodox groups which are not Protestant but which only exist because Protestantism exists) world.
The problem with this is that it is a "throw the baby out with the bathwater" situation. It is a way of engagement that says, "That looks Roman Catholic" and simply because it "looks Roman Catholic" it must be bad, or is viewed as coming with every other thing that either Roman Catholics believe/do or else is wrongly attributed to Roman Catholics (such as the false claim that Roman Catholics view Mary as divine).
So, for example, making the sign of the cross is often viewed as a "Roman Catholic" practice by many modern Protestants, and that alone makes them look at the practice with suspicion. Even though the practice of making the sign of the cross is one of the most ancient Christian devotional practices and is nearly universal. There are differences in the way Christians make the sign of the cross, but the practice itself is a nearly universal and deeply ancient devotional practice.
The truth is that a lot of Protestantism has, largely, followed the trajectory of the Reformed tradition. I'm not saying that to speak pejoratively, but simply rather to simply describe the history and make observation. A major component of the Reformed tradition is what they call the Regulative Principle--in essence, the Reformed tradition has maintained that what is not in Scripture is not allowed. This is why, for example, the Reformed tradition has a tradition of avoiding liturgical vestments for clergy, it's why things like making the sign of the cross is uncommon or totally absent in churches influenced by the Reformed tradition, it's why there is a lack of icons and sacred images etc. This isn't followed to the same degree or in the exact same way in Reformed churches or in Reformed-influenced churches, obviously; the Puritans outlawed Christmas for example, but few Reformed Protestants take issue with Christmas.
This is markedly different than how the Lutheran tradition approaches things; we instead speak of the Norma Normans and Norma Normata. We have the Norming Norm aka the Unruled Rule of Scripture, the Norma Primaris or Norma Decisionis, the norm and rule which rules over all other things; and we have the Normed Norm, the Ruled Rule, the customs, practices, traditions, confessions (etc) which are secondary, ruled over by Scripture. Which means, for example, just because Scripture doesn't mandate something doesn't mean it's wrong, if it is good and beneficial--even though Scripture doesn't mandate it--then there's no reason to do away with it. That's why Lutherans retained Confirmation, not as a Sacrament, but as a "Churchly Rite" because it served a good and beneficial purpose within the Church. It's why we didn't get rid of icons and images, it's why we didn't do away with vestments and paraments. It's why Protestants more familiar with the Reformed side of Protestantism will say that Lutherans/Lutheranism looks "very Roman Catholic"--because we didn't feel any reason to change what didn't need to be changed.
Put another way, it's been said that Luther opened the cabinet and only took out what he thought shouldn't be in there, Calvin opened the cabinet and took everything out and only put back what he thought should be in there.
A casualty of this has been that very good things, like the basic Christian belief that Mary is the mother of God is now viewed with suspicion rather than simply accepted for what it says and means.
It means there are normal Christian things which don't seem normal for many Protestants, because somewhere along the way somebody either didn't understand it, or else was too worried about "looking Catholic" and so it got ousted.
Sometimes this doesn't result in a huge problem, but sometimes it is a huge problem. And this is an example of where it's a huge problem. Because many Christians today are now basically trying to re-invent the wheel, or engaging in debates and arguments which were already had and addressed and even SOLVED fifteen hundred years ago.
Imagine having to constantly have the same argument and debate again and again over something like the Trinity because anytime someone said "Jesus is God" we had to have this whole messy debate that yes Jesus is God, but no Jesus isn't God the Father because someone, another Arius, is all "Nuh uh! Jesus isn't the Father! Let me try and fix this by making up my own theology about how Jesus is a secondary God etc etc" When we all have a shared understanding of elementary doctrines of the faith, like the Trinity, these problems don't arise. And that means we can actually get around to more important things, like preaching the Gospel, and loving our neighbor. But when we're constantly having to define and redefine and redefine and redefine and redefine everything, then we're wasting time. Not because defending the faith is a waste of time, but having to rehash every single minutia of theology every ten minutes ultimately takes away from what the Church should be doing: Being the vehicle through which Jesus Christ encounters the world and loves the world and saves the world.
-CryptoLutheran