Hi leather-watch,
I can't reproduce this here with a R25 version.
Make sure you have not enabled the region Tool.
If you copy the object with the problem into a new file, does it continue to move unselected Keyframes?
Can you reduce the file (a copy) to a single object with keyframes, and attach it here as a c4d file direct (< 1MB is the limit)
(Cloudservices: Dropbox, WeTransfer, Google, Apple, and Adobe, no zip/rar, no tiny URL, URL pasted into the text as is, no http wrapper)
All the best