Runner unable to fetch with Shell executor due to "Problem with the SSL CA cert"

When fetching a project with a shell executor, the job fails with Problem with the SSL CA cert, but the initial cloning of the repository succeeds when the first job is executed. It looks very similar to #2950 (closed)

[0KRunning with gitlab-runner 12.1.0 (de7731dd)
[0;m[0K  on domain.com ixrMAxL2
[0;msection_start:1564366732:prepare_executor
[0K[0KUsing Shell executor...
[0;msection_end:1564366732:prepare_executor
[0Ksection_start:1564366732:prepare_script
[0KRunning on glci3...
section_end:1564366732:prepare_script
[0Ksection_start:1564366732:get_sources
[0K[32;1mFetching changes...[0;m
Reinitialized existing Git repository in /var/www/gitlab-runner/builds/ixrMAxL2/0/web/site/.git/
fatal: unable to access 'https://domain.com/web/site.git/': Problem with the SSL CA cert (path? access rights?)
section_end:1564366732:get_sources
[0Ksection_start:1564366732:upload_artifacts_on_failure
[0Ksection_end:1564366732:upload_artifacts_on_failure
[0K[31;1mERROR: Job failed: exit status 1
[0;m

https://gitlab.zendesk.com/agent/tickets/127808 (for internal use)