Face based families are model with the host face at the reference plan (i.e. ground plan).
For face based families designed to be mounted on vertical surfaces (like walls), the family thumbnail orientation doesn't look right.
Orientation in the model
Orientation in family thumbnail
Change the orientation of the view cube.
The first thing is to hide/get rid of the "face" (extrusion) in the template. Select the extrusion geometry, under the properties and assign it to the "Hidden Lines" sub-category.
Go to Visibility Graphic (VG) and un-check the check-box of the Hidden Lines.
And you should get something like this:
Next is the tricky part, in the same 3D view, click the down arrow next to the viewcube and select options.
(You could also access options from the Revit "R" icon)
From the options setting, under ViewCube, un-check the check-box "Keep scene upright"
Once this is done, you should be able to twist/rotate your 3D view and turn the view sideway (Tips: it will take a few times to get used to do this) and you should get something like this:
Make sure you use the "save view" from the viewcube setting so Revit will remember this view. I usually have this as a duplicate view called "Preview" or something just to use it for my thumbnail.
The last step is to save the family. During the "save as" window, go to options and make sure you choose the thumbnail preview source as the default view.
Having done so will generate a nice and clean preview in both window explorer and your third party Family Browser: