VERIFIED SOLUTION i
Products affected: MapInfo Pro™
A common request for MapInfo Pro users is the desire to export workspaces, thematic shades, layouts , etc. to an ESRI format like .SHP.
Currently, this is not possible with current versions of MapInfo Pro.
There has been some preliminary work regarding converting styling from tab files into the "QGIS" GIS program but Support is not aware of conclusive work regarding ESRI software in a similar fashion..
A theme associated with a table is stored in the metadata section of the tab file.
Support is not aware of any software besides MapInfo Pro that has the ability to deal with this proprietary metadata format.
The best current workaround is to manually duplicate any thematic stylings, layouts, etc. directly in the ESRI program
until a more advanced conversion is possible.
The crux of the conversion problem is that MapInfo Pro does not specify how styles are applied and saved the same way as ESRI software.
Note that this issue applies in both directions - converting styled data from ArcGIS into MapInfo Pro is also not currently possible.
UPDATED: March 13, 2018