Well, for one, there's
/etc/shadow, which has all your local user accounts' (encrypted) passwords.
Like any security decision, though, this is a risk/reward tradeoff with no simple yes/no answer. It really depends on what level of security you need for the machine(s) you're managing, balanced against how badly you love the features bitbucket provides that you can't get by just replicating the repo to another machine you control.
What bitbucket features do you find useful for your /etc repo (as opposed to the alternative of replicating it somewhere else) and why?
Who might want to compromise your machine's security and why? (Looking through your bitbucket repo for information that might help infiltrate your machine would only be done by someone specifically interested in your machine, not by the usual generic vulnerability-scanning borg-like botnets on the public internet)
How much value do you place on the security of your machine and why?
Those are the kinds of questions you need to answer in deciding whether to trust Bitbucket's locked mode.
To be honest, for most minor/home/project/hobby systems, I'd probably go with yeah, keep it on bitbucket, if it has some features that you like. Bitbucket's security is probably not worse than yours.
Otherwise, just replicate it to some other machine you have more control over.
By the way, kudos for putting /etc under version control.