Fitbod Elite is implemented as an Apple "In-App Purchase", which Apple does not allow to be shared with Family Sharing. Apple lets you family share Paid-Up-Front apps and any apps you download, but they do explicitly say that In-App purchases are not sharable.
For more information, please see the following Apple support page:
Implementing a Family Subscription package is on our roadmap for the future! If you have family members who would like a subscription, please email email@example.com and we can offer them a discount code.