I assume when you use the term CRE you're actually referring to the Commission on Racial and Ethnic Disparity (aka the Sewell Commission) and not the long abolished Commission for Racial Equality. As I'm sure you know the conclusions of the Sewell Commission are not universally accepted.
The bit I've bolded is nonsense on stilts.
The term BAME is criticised for being insufficiently specific and for a variety of reasons no longer helpful:
https://equalities.blog.gov.uk/2022/04/07/why-we-no-longer-use-the-term-bame-in-government/
It might though still be useful, in the absence of an agreed replacement, as a cover all term. I used it in that context.
You cannot show where it's been said to be offensive can you?