We have run into the same issue before. Many third party services like Optimizely for example just stuff all their tracking information into a cookie, serialized as JSON, which you as the site owner don't really have much control over.

The problem is not that they wouldn't be able to parse the cookie, it's that Akamai edge node web server (Nginx or Apache, don't remember) rejects any request with a header that's above a certain size. Your origin server doesn't even get to know that there ever was such a request.

See https://maxchadwick.xyz/blog/http-request-header-size-limits for example.