Are TAGS files expected to be checked in into git, or are they gitignored?
(They are binary files, so I wasn't sure what the best practice is)
No, in general you would not check in the TAGS file. The reason is that it's not source code, but it can be easily derived from the source code.
Just like you don't (normally) check in object files or built executables because they can be recreated with a build command, you don't check in the TAGS file because it can be recreated using the ctags command.