This page (https://trello.com/en-US/guide/team-administration) seems to indicate that if you have linked a Slack team you should be able to self-join a Trello team. The section called "Be a Slack(er)" has the details.
Additionally, there is a tip that says:
> #TrelloTips: Business Class team admins can choose whether any member of a linked Slack team can join the team or if Slack team members should only be invited manually.
The current configuration for my team is: "Slack team members can self-join this Trello team." which implies that I need Business Class if I want to disable that functionality.
However, self-joining does not seem to work. How do I figure out what's wrong.
I responded to this previous question: https://community.atlassian.com/t5/Trello-questions/Trello-Slack-integration-self-join/qaq-p/1003101 but it's marked as answered so I'm not sure that it will get looked at thus the repost.