That's happened to mine a few times. I ignore it. Your blossoms look fine, so make sure the plant has all the nutrients it needs and the fruit should come out OK.

Do they look anything like mine? Mine are all turning yellow. It's been really hot and dry here and I water them but I wonder if they're not getting enough water?

Here is a link that might be useful: {{gwi:53032}}

Just be glad they don't have mildew.

I wish I could help. I have had something similar where the leaves just turned to white crunchy paper.
Definately took a toll on production. Never figured out what it was.

@lilcee, they look just like yours, but it's definitely not that they're not getting enough water. I'm pretty sure it's angular leaf spot, and have been treating it with every recipe in the book. I started with neem every week, no improvement, then I tried compost tea for 3 weeks, and it just kept getting worse.I tried copper fungicide for 2 weeks and a small improvement maybe? but then it started raining every day. I tried baking soda, but it hasn't been dry for days so I can't tell if that was effective. I've decided on switching between milk spray and baking soda, and if it doesn't improve I'm pulling up the plants and putting down butternut squash!