Grounding or interference issue with MacBook's Type-C ports and external monitor

I'm having a strange problem with my external monitor.

My MacBook is connected to the monitor via a Type-C → DisplayPort cable—the image works fine. But when I connect the charger to the other Type-C port on the MacBook and touch the MacBook with the charging cable, the image on the monitor momentarily disappears.

If I hold the cable so it's constantly touching the MacBook, the image flickers and then appears permanently. As soon as I remove the Type-C cable and touch the MacBook again, the flickering returns.

It looks like a grounding or interference issue between the DisplayPort and charging ports. Has anyone else experienced something similar? Is there a solution?

[Re-Titled by Moderator]