What causes stringy winter squash? I know that spaghetti squash is supposed to be stringy; this question is not about that.

When I cook winter squash, I cut the squash in half, remove the centre (seeds/strings), rub the flesh with olive oil (sometimes stuff the cavity with stuffing), and bake in the oven for 30-40 min at 350oF until tender.

However, I notice that pretty much all of the acorn and butternut squash I bake comes out stringy and tasting awful. It's gotten to the point where I don't buy them anymore, because I wind up throwing it out. I'm not sure if it's because I'm purchasing unripe squash or if it's because I'm cooking them wrong (although I have cooked many an acorn and butternut squash this way for years without problems up until about a year ago).

I don't seem to have this problem with buttercup squash (which, in my opinion, is much tastier, but harder to find in my area). Somehow I doubt that all of the acorn and butternut squash in the Chicagoland area is somehow just bad, although I have tried purchasing these types of squash at many different grocery stores and even farmers markets to try to see if it was an issue with a particular store.

Are the squashes I'm cooking with underripe? Overripe? Is it a cooking problem? How can I ensure that I'm buying a good acorn or butternut squash when I'm at the grocery store?
Well it's possible they are over ripe. Acorn squash should be dark green or mostly so when it's ready to eat. It turns orange when it's ripe, but just like many circubits and cucirbits (squashes and melons(including cucumber)) you don't want to eat them when they are ripe, you eat them before they start to ripen.

How you store them makes a difference in the long term but not so much in the short term. Last year we had a batch of acorn squash that was thin and stringy and not tasty just like you described. I think they didn't get enough water at the farm that grew the Walmart acorn squashes.

On the other hand, I have held on to acorn squashes for 2 years in the cool, and dark and they were still quite tasty.

Just try again, but try a different source for them for now.