I am experiencing the same problem. The map is clipped and displays perfectly in ArcGIS Pro, but once exported (mine to jpg/png), some layers still extend beyond the defined clipping shape. I found a workaround this issue. I made a copy of one of the layers that showed beyond the clipping boundaries in the export, changed its symbol to no fill and no stroke line. Called it Dummy, I then excluded the Dummy layer from the clipping. It somehow made the other layers disappear from the exported png file.
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