I have my desktop report set up to show data labels on one item but not another in multiple visuals. When published to BI Web, it shows all of the data labels, even those I don't want. When I try to "edit report" in BI Web, it won't let me turn the data labels off indivudually.
Yes, my company is currently experiencing this situation too. On Monday, 4/22/19, some pinned visuals on a dashboard mysteriously gained data labels that had previously been removed via the customize series option in data labels. This happened on a line and stacked column chart. We have always had the line value data labels turned off but now they can't be removed. The column labels don't seem to have the same issue. We re-published the report from Power BI Desktop (without labels on some series) and the service continues to show all data labels.
4/26 Edit: Our dashboards and reports in the service were back to looking normal on Wednesday 4/24.