It matters little what the Campbells believed or taught.
However, it is important to grasp that the Restoration Scholars believed what the historic trinitarians believed:
They believed in the one God in heaven
And one Lord on earth.
"and we believe in the holy spirit."
None of the creeds ever used the word personae to mean 'person' in the very modern view of PERSONS which would be blasphemy if applied to the One God of the Universe.
Thomas Campbell notes that: "Is it farther queried, how could the Father bring forth or exhibit his Son in human nature, or how could divinity and humanity be so united
as to constitute but one individual person? We might as rationally query,
how can soul and body, matter and mind be so united as to make but one individual being or person?
"It appears to be a query with some who profess to hold this doctrine, whether it be correct to use the term person when speaking of the above distinct characters (personae) in the divine essence. As to this, let every man be fully persuaded in his own mind. In the mean time, all that we pretend to say in favor of this application of the term is,
<font color="#FFFFFF">..... that although the term person (which, in relation to men,
.....signifies a distinct intelligent agency or rational being,
.....coexisting with others in the same common nature),
.....is not manifestly applied in the Holy Scriptures to any of the Sacred Three:
.....nor indeed can be so applied in strict propriety, according to its literal and obvious acceptation;
for when applied to God, instead of meaning a distinct intelligent being coexisting with others in the same common nature,
we must mean by it, if we think and speak correctly, one and the self-same individual being so existing as to constitute in and to itself so many distinct or different, real and relative characters, or subsistences,
each of which is but another name for the self-same individual essence or being considered as existing in the specified relation of Father, Son and Holy Spirit.
"Yet seeing the Scriptures manifestly declare that the one Jehovah exists in three distinct intelligent agents,
.....each of which is the one Jehovah so existing, for there is but one such being;
and seeing that the personal pronouns, I, thou, he, we, us, are assumed and used in the Holy Scriptures, by, or in relation to, each or all of the divine characters; therefore, keeping in view the essential
.....and indivisible unity of the divine nature,
we think that we speak intelligibly and consistently with sacred truth, when we thus use the term person; and we presume, when taken in this sense, it will apply to the divine characters with as strict propriety as almost any other term in human language that is applied to God; for it must be granted, that in but few instances, if any, human language will strictly and property apply to the divine nature;
.....therefore, when so applied, it must, for the most part, be used in a figurative and analogous sense.
"Again, it is a query with others, who profess to hold this doctrine, whether the relative terms Father, Son and Spirit, be real or economical. To this we would reply, that if we allow the Holy Scriptures to speak at all intelligibly upon this most profound and sacred subject,
.....we must understand the above appellation as declarative of real internal essential relations,
.....independent of any external work or economy whatever.
"For if the terms Father, Son and Spirit, be not declarative of real or essential relations, that is, of relations that have their foundation in the divine nature, and essentially or necessarily belong to it as such,
.....the Scriptures do not reveal to us three distinct characters so related;
.....but three distinct independent divinities or Gods, necessarily self-existent, and absolutely independent of each other; each and every one of them possessing the self-same properties,
and of course, each of them so exactly the same in all respects, as to be absolutely undistinguishable one from another, by any means, property or attribute whatsoever;
and, of course, three eternal self-existent independent coexistent Gods;
each of them infinitely complete or perfect in and of himself, as possessing every possible perfection of being.
"A supposition this, not less repugnant to our reason than to the most express and unequivocal declarations of Holy Scripture, for the divine characters are constantly represented as coexisting in the most intimate and inseparable unity of essential relationship..
"And that, therefore, in the mean time, we ought to reject as unscriptural, all invocations or forms of address immediately directed to the Holy Spirit, as innovations in the worship of God, who alone has a right to prescribe both the matter and manner of his own worship, even of that worship which he will be graciously pleased to accept as right and pleasing in his sight. (Memoirs of Alexander Campbell, Vol. 1, pp. 539-555.
We don't have to go beyond clear statements by the Bible that there is only ONE GOD and one mediator between God and man, the man Christ Jesus. We, in fact, deny the majesty of the Work and Word of God through Jesus if we do not just PREACH about the trinity by READING the Word.
John Mark Hicks and LU so defines the trinity which was "repugnant" to the Campbells by putting words into their mouths.</font>
Alexander Campbell the Trinitarian System.
1. In the first place I object to the Calvinistic DOCTRINE of the Trinity for the same reasons they object to the Arians and Socinians.
They object to these, because their views derogate in their judgment from the eternal glory of the Founder of the christian religion.
ARIANS & SOCIANS: They will not allow the Saviour to have been a creature, however exalted,
.....because they conceive this character is unbecoming him, and contrary to the scriptural statements concerning him.
.....They wish to give him more glory than they think the Arians are willing to do.
Now I object to their making him and calling him an
....."Eternal Son" because I think that if he were only the Son of God from all eternity,
.....he is entitled to very little, if any more glory, than what the Arians give him.
CALVINISTS: I wish to give him more glory than the Calvinists give him.
They are as far below his real glory, in my judgment, as the Arians are in their judgment.
2. But in the second place, I have an insuperable objection to the Arian and Calvinistic phraseology--
On the doctrine of the first relation existing between the Father and the Saviour of Men,
.....because it confounds things human and divine,
.....and gives new ideas to bible terms unthought of by the inspired writers.
The names Jesus, Christ, or Messiah, Only Begotten Son, Son of God, belong to the Founder of the christian religion, and to none else.
They express not a relation existing before the christian era, but relations which commenced at that time.
To understand the relation betwixt the Saviour and his Father,
.....which existed before time,
.....and that relation which began in time,
.....is impossible on  either of these theories.
There was no Jesus, no Messiah, no Christ, no Son of God, no Only Begotten, before the reign of Augustus Cesar.
The relation that was before the christian era,
.....was not that of a son and a father, terms which always imply disparity;
.....but it was that expressed by John in the sentence under consideration.
The relation was that of God, and the "word of God."
.....This phraseology unfolds a relation quite different from that of a father and a son-
.....-a relation perfectly intimate, equal, and glorious. This naturally leads me to the first sentence of John.
.....And here I must state a few postulata.