Website with different coloured navigation per product page

I have a client asking me to change the navigation colour scheme on a website design im doing to match the individual products.

Personally I think its:

  1. a bad idea
  2. it wont work with their overarching brand
  3. it is confusing
  4. just a bad experience.

They have seen the Barbican website which they really like and wish to replicate the navigation colour style here utilising the branded products.

Background:

This brand, for the sake of this being public lets call it 'X'.

The site is relatively small and X are only selling 7 products right now and the range will likely grow at a very slow rate, each product is branded with a different colour scheme to distinguish it from the rest. This is something I can not change. They also want this to be AA accessible too.

Question:

Are there any studies or research that can back up the suggestion as to why this is a bad idea? Or have any advice that I maybe missing here that I can back up my rationale with.