Issue with NGINX FastCGI Caching

I have a page, with an embedded YouTube video which can be found at https://aticornwallinnovation.co.uk/ocean3d/

Once you accept cookies, I expect that the YouTube video should be visible, but it does not.

Digging into this, it appears to be a caching issue. The server in question uses NGINX FastCGI caching. The server does cache urls containing a query parameter, so as an acid test, I visited the same page with a random parameter: https://aticornwallinnovation.co.uk/ocean3d/?hello-youtube

…And the youtube video appears.

What can I do to have this plugin work alongside NGINX FastCGI caching?

The page I need help with: [log in to see the link]