I've had something similar, although not exactly the same happen. It started when I installed the latest game update (which was just at the beginning of this week- I hadn't played in awhile).
After my sim gets out of the shower, she does the spin around thing with the sound effect (like she's putting clothes on... you know what I mean), but she doesn't actually put clothes on. She does have the privacy pixels though. She then proceeds to go about her day completely naked. So far, when I've manually had her change into clothes it's worked. I've only played one other game file since I started having this issue, but so far it's just affecting the one sim.
I also have no custom content or mods whatsoever. I do have some official store content, but that's it. I just assumed it was some sort of weird glitch with the latest update.