Can I keep cut-up raw butternut squash in the fridge, and if so, for how long?
Yes. Cover it -- put it in a container, ideally -- and you can keep it for at least 4 days.
Does the same hold true for cut-up peeled sweet-potatoes?
Any potato, russets, yams will keep in the fridge without turning brown if you have the pieces submerged under water.
One of the farms at our wintertime farmers' market sells, in addition to whole squash, bags of peeled and seeded butternut squash segments. I bought some last year on a few occasions, and it kept well for several days in the fridge in its plastic wrapping.
Sweet potatoes brown after cutting, so I wouldn't store them this way.
I bought fresh butternut squash to make baby food. How long can I keep it uncooked in refrigerator????
If it is cut up, see discussion above. Whole butternut squash is nor normally refrigerated, but it also is traditionally a cool weather crop and stores well. I don't know if refrigeration would help or hurt storage this time of year. For general info here is a pretty good page: https://www.thebalance.com/how-to-store-butternut-squash-1389335
you will also get lots of hits if you Google storing butternut squash.