As far as Christadelphian anti-trinitarianism goes, there is no doubt about the Christadelphian position. The Holy Spirit is the power of God, not the third person of the Trinity. If asked to explain the Christadelphian theology of the Holy Spirit most Christadelphians would have no difficulty in explaining what the Holy Spirit is not - and would be acquainted well enough with sufficient texts to demonstrate that it is the power of God.
The difficulty for many Christadelphians is that their theology (or more precisely their pneumatology) has never been sufficiently developed to explain how this 'power of God' works today in the lives of individual believers, and some Christadelphians have complained over the years that their community does not provide good resources for understanding the subject.
In fact, controversies about the subject (especially in the 1960s and 1970s) led to division (especially in Australia where ecclesias were divided into two groups which were 'out of fellowship' with each other for many years while both groups claimed to be in the 'Central fellowship'). For fear of the consequences many people simply didn't discuss their views on the subject and almost an entire generation grew up with a poor understanding of the role of the Holy Spirit today.
It is sometimes claimed that Christadelphians believe the Holy Spirit is not active today in the life of the believer, that the gifts have ceased, and that there is no such thing as the 'indwelling' of the Holy Spirit beyond having an intellectual understanding of the Bible (and some Christadelphian groups have equated the Spirit of God with the Word of God - by which they mean the Bible - to such an extent that they refer to the Spirit-Word and read almost every reference to the Spirit to mean the Bible).
However, none of these propositions are stated in the Birmingham Statements of Faith (either amended or unamended). To the contrary, the Birmingham Statements of Faith positively affirm that an indwelling of the Holy Spirit is required in order for God to be manifest in believers.
What the BSF actually says about the subject is this:
1. That the only true God is He Who was revealed to Abraham, Isaac and Jacob, by angelic visitation and vision, and to Moses at the flaming bush (unconsumed) and at Sinai, and Who manifested Himself in the Lord Jesus Christ, as the supreme self-existent Deity ...
2. That Jesus of Nazareth was the Son of God, begotten of the Virgin Mary by the Holy Spirit, without the intervention of man, and afterwards anointed with the same Spirit, without measure, at his baptism.
10. That being so begotten of God, and inhabited and used by God through the indwelling of the Holy Spirit, Jesus was Emmanuel, God with us, God manifested in the flesh - yet was, during his natural life, of like nature with mortal man, being made of a woman of the house and lineage of David, and therefore a sufferer, in the days of his flesh, from all the effects that came by Adam's transgression including the death that passed upon all man, which he shared by partaking of their physical nature.
What these statements clearly say is that God was manifested in the flesh by Jesus :
1. being begotten of God
2. being inhabited and used by God through the indwelling of the Holy Spirit
If Jesus is our example/model, the "firstborn among many brethren", then it follows that there is only one way we can manifest the Father, viz. by being:
1. born again, born of water and Spirit, so that we become childen of God
2. inhabited and used by God through the indwelling of the Holy Spirit.
It amazes me that so many Christadelphians seem to have missed what is so clearly spelled out in their own statements of faith.
A proper study of the Holy Spirit and its role in the lives of believers is well overdue. Some progress was made in this direction with the short work published by "The Christadelphian Office" (The Christadelphian Magazine and Publishing Association) entitled "The Holy Spirit and the Believer Today" (A.D. Norris, 1975) This work has apparently been out of print for some time and may even be an embarrassment to the current editor who seems to have a different view on the subject and may be reluctant to admit that Christadelphian doctrine (at least the way it's explained by the CMPA) appears to have changed on this point. Edgar Wille's excellent studies "The Holy Spirit - an exploratory survey of Scripture teaching" (first published 1975, reprinted 2000) is undoubtedly the best work on this subject to be published in the Christadelphian community and deserves to be given careful consideration.