What I am looking for is something similar to the GitLab functionality:
Merge commit with semi-linear history
A merge commit is created for every merge, but merging is only allowed if fast-forward merge is possible. This way you could make sure that if this merge request would build, after merging to target branch it would also build. When fast-forward merge is not possible, the user is given the option to rebase.
As far as I can see, this is currently not possible to configure in Bitbucket. Further I would like a setting that I can use to enforce this in the UI.