On the server where Jenkins is running, I used
sudo setfacl -m user:tomcat:rw /var/run/docker.sock
And then run each docker container with
-v /var/run/docker.sock:/var/run/docker.sock
Using setfacl seems a better option, and no "-u user" is needed. The containers then run as the same user that is running Jenkins. But I would appreciate any feedback from the security experts.