It looks like this bug is back in release: EPiServer.CMS.UI 11.29.0
Hi Erlend!If you look at the release notes for EPiServer.CMS.UI 11.30.0, they have fixed another bug that claims sort order should be used: CMS-16067Maybe CMS-13481 and CMS-16067 are in conflict. Prior to CMS-16067 being «fixed» sort order only affected the list in admin mode.
There was an unintentional change (CMS-13481) that hard-coded alphabetical sort order of available content types (not just block types). This change was reverted in CMS-16067. If you also update EPiServer.Cms.Core, content types should not just be sorted by the order you specify but if multiple types have the same sort order then they're sorted alphabetically. As you would expect.