I suggest first verifying if the ConvertToXhtml filter is not disabled. This filter provides a logic to strip the unwanted BR tag.
If the filter is enabled, then the only possible way to resolve this browser behavior is by implementing the suggested logic by Rumen.
Note that a BR tag is added when Enter or Shift+Enter is pressed, therefore in every case only a blank new line still is blank content area. So the suggested logic should fir your requirements.
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