Upcoming Weblate 2.17 will bring improved access control settings. Previously this could be controlled only by server admins, but now the project visibility and access presets can be configured.
This allows you to better tweak access control for your needs. There is additional choice of making the project public, but restricting translations, what has been requested by several projects.
You can see the possible choices on the UI screenshot:
On Hosted Weblate this feature is currently available only to commercial hosting customers. Projects hosted for free are limited to public visibility only.