Thimbles help to maintain the correct bend radius at the end of a winch line and also help with abrasion.
Some heavy duty webbing can function to protect the line, just make sure not to use a thimble that is too small, make sure your shackle pin doesn't twist on the synthetic line too much, and such that extra abrasion doesn't occur. I still prefer a thimble for a little extra safety margin.
Multiply the width of your winch line by 4 (for Amsteel Blue, Dyneema SK 75). So 3/8" x 4 = 1.5 inches. The bend radius in your thimble or shackle pin should be no less than 1.5".
The formula may vary for different types of synthetic line.
Synthetic line can be bent pretty harshly and still function but it is happiest when pulled in a straight line. The splice and any bend, kink, etc can introduce a weak point, so keeping that 4:1 with Amsteel Blue will keep your line's strength from being degraded severely.
I run a tube thimble and then a hook. The tube thimble protects the line and the hook makes a quick attachment point to hook to a tree strap, etc. Nothing wrong though with just running a thimble and then a proper shackle.