The install sites from existing configuration feature need all the sites to have the same profile. The reason is the core.extension.yml, where the profile is defined. Drupal doesn't allow to install a site without the profile defined in that file, but nevertheless, the profile can be defined in the installation process.
Allow core.extension.yml to be imported without the profile key during the installation process, and inject the install profile as a parameter stored in the $install_state global variable.
Needs work
11.0 🔥
The change is currently missing an automated test that fails when run with the original code, and succeeds when the bug has been fixed.
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It's likely this issue predates Contrib.social: some issue and comment data are missing.
I fully agree that this needs to be reviewed by a subsystem maintainer. I think it is a change that could have consequences.
In the meantime I have created an RM with the latest patch so that anyone can add the tests there and make it compatible with 10.3.x and 11.x.