I think the average layperson in a Protestant church probably has a rather deficient understanding of the Trinity, but that doesn’t mean the official teachings of his denomination are heretical, no more than the similar ignorance of the average Catholic would make official Catholic teaching on the Trinity heretical.
I would say all of these that deny “Theotokos” to St. Mary are deficient in their theologies of the Trinity, and most especially of their understanding of the Word Incarnate/God the Son. Those that baptism in the name of the “Creator, Sustainer, and Redeemer” are way off, as these are actions of the Trinitarian God not necessarily individual Persons. The teachings of some denominations that Christ’s mediatory power only extends to this life, and once a soul enters the next life they can no longer be prayed for or with - this is heresy because it limits God and Christ’s Incarnation/Crucifixion/Resurrection.
The Lutheran position, from the Augsburg Confession:
Article I: Of God.
1] Our Churches, with common consent, do teach that the decree of the Council of Nicaea concerning the Unity of the Divine Essence and concerning the Three Persons, is true and to be believed without any doubting; 2] that is to say, there is one Divine Essence which is called and which is God: eternal, without body, without parts, of infinite power, wisdom, and goodness, the Maker and Preserver of all things, visible and invisible; and 3] yet there are three Persons, of the same essence and power, who also are coeternal, the Father, the Son, and the Holy Ghost. And the term “person” 4] they use as the Fathers have used it, to signify, not a part or quality in another, but that which subsists of itself.
5] They condemn all heresies which have sprung up against this article, as the Manichaeans, who assumed two principles, one Good and the other Evil: also the Valentinians, Arians, Eunomians, Mohammedans, and all such. 6] They condemn also the Samosatenes, old and new, who, contending that there is but one Person, sophistically and impiously argue that the Word and the Holy Ghost are not distinct Persons, but that “Word” signifies a spoken word, and “Spirit” signifies motion created in things.
The Catholic response to this in the Confutation:
To Article I.
Especially when in the first article they confess the unity of the divine essence in three persons according to the decree of the Council of Nice, their Confession must be accepted, since it agrees in all respects with the rule of faith and the Roman Church. For the Council of Nice, convened under the Emperor Constantine the Great, has always been regarded inviolable, whereat three hundred and eighteen bishops eminent and venerable for holiness of life, martyrdom and learning, after investigating and diligently examining the Holy Scriptures, set forth this article which they here confess concerning the unity of the essence and the trinity of persons. So too their condemnation of all heresies arising contrary to this article must be accepted - viz. the Manichaeans, Arians, Eunomians, Valentinians, Samosatanes, for the Holy Catholic Church has condemned these of old.
Since you did mention Methodist, I can at least try to comment on them. Going through Sunday school, I remember being taught the trinity or have it explained that would be similar to the teaching of Catholic Church. I think most mainline Protestant denominations do hold as a basis similar teaching of the trinity like the Catholic church. From what I know about Baptist (which is a pretty broad group), they hold as well to the trinity and a traditional understanding. I think where Protestantism begins to stray is in independent, non-denominational churches, especially those influenced by WoF movement. There sound Christian doctrine fall victim to “revelations and visions” and anything goes.
Every protestant I know personally in mainstream churches, as you specified, believe exactly the same thing as Catholics when it comes to the Trinity.
As for the “Theotokos” issue, there is no disagreement when it comes to Who Christ is, we all (in the mainstream that was specified) believe and acknowledge Him as God the Son. The issue of “Theotokos” is when is interpreted Mother of God and not God-bearer. Mary is the mother of God the Son as incarnated as Jesus, but is not the mother of God the Father, nor God the Son in His pre-incarnated eternal form. So, the quibble over semantics is about Mary, not about Jesus. I, and most other mainstream protestants, would not have a problem at all saying Mary bore Jesus, Who is God the Son, therefore is rightly called “God bearer.” The label was given to insure everyone admits that Jesus is truly God, and that is a basic belief of mainstream protestant churches.
And, I would add, those who deny Theotokos are deficient in their ability to provide apologia for Christ’s divinity.
All a, say, Muslim has to posit is: You deny Mary as Theotokos? Well, who do you think Jesus was, if not God? It would seem that you don’t actually believe that God became Man in Christ Jesus, if you can’t acknowledge Mary as the Mother of God.
There does not seem to be an adequate response to the Muslim’s query.
That is the logical conclusion of the denial of the Theotokos.