This seems new for 4.4. Having extdebug in BASHOPTS seems to change the invocation behavior to mimic that of having specified the --debugger option, which I don't think is usually the intention:
$ shopt -s extdebug; export BASHOPTS
$ bash -c 'echo $BASH_VERSION; shopt -p extdebug'
4.3.42(1)-release
shopt -s extdebug
However, in 4.4:
$ shopt -s extdebug; export BASHOPTS
$ bash -c 'echo $BASH_VERSION; shopt -p extdebug'
bash: /Users/levit/utils/stow/bash/share/bashdb/bashdb-main.inc: No such file or directory
bash: warning: cannot start debugger; debugging mode disabled
4.4.0(3)-rc2
shopt -u extdebug