Hmm. In that case, I'm not seeing it. The REB includes John 1 and Colossians 1-2, the resurrection stories, the miracle stories, and the Annunciation, all presented in a pretty straightforward way. I don't see anything in the translation that denies the doctrines you've listed. Maybe you can be more specific.
As is often the case, it is not a blatant denial of important doctrines that is presented (that would be too obvious), but a more subtle undermining of them. Verses are often worded to remove, weaken, or make ambiguous, clear references to vital doctrines.
I don't have a REB and it's not so easy to find an online version; however, here are a few examples of what I mean.
Rom. 9:5 (REB) The patriarchs are theirs, and from them by natural descent came the Messiah. May God, supreme above all, be blessed forever! Amen.
The above is worded to remove the interpretation that the Messiah is God. Compare this with Evangelical translations.
Rom. 9:5 (KJV) Whose are the fathers, and of whom as concerning the flesh Christ came, who is over all, God blessed for ever. Amen.
Rom. 9:5 (ESV) To them belong the patriarchs, and from their race, according to the flesh, is the Christ, who is God over all, blessed forever. Amen.
In these, there is clear testimony to Christ as God.
Rom. 9:33 (REB) mentioned in scripture: Here I lay in Zion a stone to trip over, a rock to stumble against; but he who has faith in it will not be put to shame.
Faith in "it"??? Clearly "it" is not supposed to refer to the Lord here. What "it"
is supposed to refer to, is anyone's guess!
Rom. 9:33 (KJV) As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.
Rom. 9:33 (ESV)
as it is written,
“Behold, I am laying in Zion a stone of stumbling, and a rock of offence;
and whoever believes in him will not be put to shame.”
These are obviously referring to a person, not an "it", in whom to believe.
There are many, many such examples, throughout the REB. It has a clear bias against the deity of Christ (and other vital doctrines).