We have a Teams group which is 'members only' in that it's only open to paying members of our internal gym. Membership of the gym is an offline process, which has to be done before we let people join our gym Team/group.
Unfortunately even with the group/team set to Private, people can (and endlessly do!) request access, even though they're not members of the gym.
Is there any way of preventing access requests, like the setting on a SharePoint group?
As far as I know, you can't prevent access requests to Groups, but what you can do, is hide a Group from the global address list in your company and from the discover option. That way, people won't be able to find the Group, unless they are specifically invited (or someone tells them the URL of the Group).
You can do that through PowerShell:
Set-UnifiedGroup -Identity "<your Group name>" -HiddenFromAddressListsEnabled $true