Don't share data between root domain and subdomain

Is there a way to stop sharing data between domains.
For example, we want to show workflows to visitors/leads on our public facing site. However, when someone visits our public facing site (www.example.com) as a visitor, they’ll see a workflow targeted for that domain.
Then if they click on LOG IN button and logs into the customer portal on subdomain (subdomain.example.com) then they’d continue seeing the workflow chatbot popup in customer portal too.
Though we don’t want the customers to see the workflow that was specifically targeted for the public facing site.

This frustrates the customers as they just want to go about their business with using the product.

I have seen so many people in community forum facing the same issue but still no solution in sight. Even the Intercom (shutdown) is also not expected solution here.