This post raises a number of separate issues.
First, I don’t think the term “modes of existence” necessarily reflects modalism. Because the term isn’t used in any official definitions, it can be used in different ways. You’d need to see how a given writer is using it. One could, for example, say that it refers to God’s three ways of existing, as uncreated, begotten and proceeding.
Indeed the whole issue of modalism is complex, for reasons I’ve only realized while watching this discussion. Lots of people have been accused of it, and they’re not all saying the same thing. The essence of it seems to be denying an actual distinction of person within the Trinity, something that can happen in various ways.
Is modern Protestant theology modalist? I think that’s hard to judge. First, one of the characteristics of modern theology, going back for at least 200 years, is that it tends to avoid the metaphysical language in which Trinitarian theology has often been expressed. If that’s enough to make something heretical, then most modern Protestant theology is heretical. If not, you have to look at what’s being said and decide whether it’s trying to get at the same thing as the traditional definitions.
There I think you’ll find two basic strands, which are often mixed.
There’s a fair amount of modern theology that tries to maintain continuity with traditional theology, using modern concepts but trying to say the same thing. Most of it is not intentionally modalist.
The second strand starts from Scriptural scholarship, and is suspicious of doctrine that strays too far from it. Many of these people think that NT discussion of the logos and other ways of speaking of preexistence are referring to something that’s not ontologically equivalent to the Father, but is more a way of speaking of God’s way of being present with his people. These approaches may be closer to the original Monarchians, though it appears that even the Monarchians had probably lost some of the Jewish background to the NT language.
However these folks may still, as I do, think that if Jesus shows us God, then that God can’t be thought of as a pure monad, but there has to be some kind of personal relationship within his existence.
The following is the most recent official statement on the Trinity by my church:
https://www.pcusa.org/site_media/media/uploads/theologyandworship/pdfs/trinityfinal.pdf. I believe it’s a representative of the first approach. Whether it actually manages to avoid modalism you’ll have to judge. Here is probably the most critical paragraph from that point of view:
“When we confess with the creeds of the universal church that God is “one in substance, and yet distinct in three persons” (The Scots Confession, BC, 3.01), we use terminology that is strange and perhaps off-putting to many members of the church today. However, the intent of these words is to declare that the mystery of the Trinity cannot be reduced either to a solitary individual or to a close-knit group of individuals. Trinitarian faith witnesses to the divine reality as living, active, dynamic, and relational. Relationship is at the heart of God’s being. One yet richly differentiated, God’s being is in communion. God lives and acts in mutual, self-giving love.”
I agree with this document, including the paragraph just quoted. But it avoids a review of the NT evidence, which I think would lead to a good deal of circumspection in how one asserts the Trinity.
