auto oil vs motorcycle oil

[TFOGGER]

For something like a TW200 or XT350, would you recommend just sticking with motorcycle specific oils?

Since they both use a little over a quart of oil each, the cost savings using diesel oil is not very great, so motorcycle specific oil is probably a good choice. Neither one is likely to particularly stress the the oil's lubrication capabilities, so pretty much any oil rated API SE-to API SH would probably work.
Ask any 4 guys about opinions on oil, and you'll get 5 answers. I believe engineers know what they're designing the oil to do, and buy my oil accordingly.