I suspect you will benefit from watching this Think Data Thursday video
It doesn't answer your specific question regarding WMS, but then Mapbox might be a better solution for you anyway. In 9.2 Mapbox will be 'integrated' in Tableau.
Hope this helps.
Tableau only supports WMS maps in lat/long (plate carree) projection which gives the distortion you see.
Tableau does support maps in Web Mercator projection such as the default background map, but not from WMS currently.