I have recently set up a Joomla 3.9.5 website and installed CMC Mailchimp for Joomla v 3.03. I have set up a mailchimp account, created a list, copied across the API key...
In Joomla's backend when I select Components->Newsletters->Lists, I see the list I established in Mailchimp. When I click on the "Add Users to lists" button I see a warning saying "NOTE: Adding users will take some time. An average value is 50 users per second, which means adding 3000 users will take about one minute. Adding users again, which are already in your list, will update their merge fields and interest categories but will also reset the merge field "date added (API)" to today's date, which might get your autoresponders in trouble! " There is a little timing icon going round and round, but nothing happens after that. I only have 3 Joomla users, and one mailchimp user, so there is a problem.
If I push things along, select a user and click the "Add to Mailchimp" button and select "Selected users", then I get an error "Error:1 Errors: Table 'faithf84_joom581.#__community_fields' doesn't exist => firstname.lastname@example.org)". Maybe this error is a result of the earlier problem, or a symptom.
The Joomla site is hosted on siteground.
The other thing that doesn't seem to be working is the link between the design of the subscribe box in Mailchimp and in Joomla, although registering through Joomla does seem to work.