Windows 7. Here's a confounding fact I noticed after posting. Both of my computers run Windows 7 and are up-to-date. Both were somewhat recently clean-installed and are only used for non-Linux software. I was able to login fine with the laptop, but not the desktop. If I remember the wording from the desktop's certificate viewer correctly, it said that the certificate from Let's Encrypt was recognized as a valid certificate, but the root authority DST Root CA X3 was not recognized. After going through the steps for adding DST Root CA X3, the login worked on the first try.
In other words, no I wasn't making that observation because the name didn't include "Let's Encrypt".
To say it's a "somewhat common" problem with Let's Encrypt is probably an overstatement, but it is definitely not unheard of. I found many threads about "Could not check ssl certificate status" issues with the common factor between my problem and theirs being a Let's Encrypt certificate that wasn't accepted. (That's not to say the cause was always the same.) If I had used Windows more, I would've eventually run into problems on other sites that rely on DST Root CA X3.