I received a ding for not answering a message within 24hrs when I actually answered him right away, AND it wasn't even a buyer. It was a message from a seller that I purchased items from. Not sure how that even showed up in the star seller area. It took me to 94% when I'm usually 100% on answering promptly.
"It was a message from a seller that I purchased items from."
They count. Always have.
Etsy is pretty clear about how the message response rate is calculated in help center here https://help.etsy.com/hc/en-us/articles/4403058372503-How-to-Become-a-Star-Seller?segment=selling
There is a highlighted bit under message response rate info that says "The Message response rate only applies to the first message in a thread. Initial messages from both buyers and sellers on Etsy are counted towards the Message response rate. "
That means ALL messages. It also means each individual message thread so if someone sends you 5 different messages with 5 questions instead of putting them in the same message chain you need to respond to all 5 of them. The system is completely automated and doesn't know if the message is from a buyer or another seller. It just sees a message and calculated the response time. That's just how it works.
The info is also right there on the Star Seller page in shop manager. Just go to shop manager > star seller. Once there scroll toward the bottom until you find "Questions? We've got answers." Then click messages. The very first question there says
"What messages count toward the message response rate?
Your message response rate is based on just the first message in a conversation, not ongoing conversations. This means you just need to respond to the first message within 24 hours. This applies to messages both from buyer and seller accounts. Messages from Etsy staff do not count toward your response rate, and neither do messages that you mark as spam. You can also now find a breakdown of your message response rate score by downloading a CSV."
You can try marking the message as spam now and it should be removed from the calculation in a few days.
If the star is important to you then it may be a good idea to read or review all the info Etsy provides about the star seller program.
Bottom line...you have to either reply or mark as spam.