Yeah. So which diff? In a Crosstrek or Impreza, there are three. The only one that concerns us here in a Subaru transmission is the one in the transmission itself. The center and rear diff disappear when building a Speedster with either mid or rear engine configuration. Subaru does a cool thing with the transmission and has two shafts running one inside the other going to the center diff. A special piece is made to eliminate the diff and shorten the transmission, which also turns the transmission into two wheel drive instead of all four. A new and custom cover makes it a pretty slick option.
I've no idea if the FRONT diff in a Crosstrek is TBD(can we please use this term instead of LSD?). Say it after me: torque biasing differential.
I do know that in a rear-engine configuration the Suby trans gets a reverse ring and pinion allowing the Subaru trans to be installed and work in this position. You CANNOT simply flip the diff in a Subaru like you do in a VW.
Now, onto VW options. Yes, it is MUCH easier to simply use a properly geared VW trans with bellhousing/clutch adapter to Subaru. However, you'll have 4 speeds. The 5 speed options are both expensive and more difficult, but doable with wheelbarrows of cash. Same goes for the Subagears diff in a Subaru in a rear-engine installation. All you need to do is add the money.
You could also use a Porsche 901 or 915 trans. Add even MORE money.
I have almost 200 hp in a 1500 pound Spyder with an open diff VW 4 speed. With proper suspension setup and STICKY tires, you simply don't need a TBD or LSD or any of that fluff. Unless you drive it(or over-drive it?) on the track well beyond the limit of what most mortals here(including me) can drive.
If I start to hooning and say rev it up and dump the clutch, I lay down two equal and even patches, even with an open diff. Stop the madness, you don't need it.