Hi Andreas,
Unfortunately this is not currently possible in Kibana. However, there is already an enhancement request for it over here: https://github.com/elastic/kibana/issues/9550. If you have a GitHub account, I would encourage you to add a comment there about your use case (that is, why you would like the disable / hide the x-axis bar labels) — this will help increase the priority of this enhancement request. Thanks!
Shaunak