Hm … this seems like no Docker issue at all !
First of all, if your Docker container host’s any Linux OS, any “directorynames” are always case-sensitive ! Contray to Windows. So assuming your folders are kept in lower-letters (all the time !) you could use e.g. ‘awk’ to convert the dir-string to all lower letters. Something like this:
$ echo "$include" | awk '{print tolower($0)}' > ~/.inputrc
Second: The error message speaks of an “unknown operand”. As this is (most likely) a bash shell, set completion-ignore-case On is not a valid shell command !