Seems like an odd software choice to create actual dotfiles under /etc. Often files there have much the same name as a user's dotfiles but without the dot. Thinking of things like /etc/profile vs ~/.profile and so on.
Without knowing precisely why those decisions were taken (good reason? ignorance? insanity?) it's not clear what steps to take.
Vaguely leaning towards symlinking or hardlinking but precisely what to do and which way around is still unclear.
Do those dotfiles have your user permissions or are they owned by a system account like root?
Then they shouldn't have dots on them (bad design decision) and should be backed up by the system backup/restore mechanism, whatever that might be, not the user's own homedir backup, which is what I assume OP is talking about.
If they're talking about a full system backup including home directories, that's a moot point because I'd expect they'd be included anyway, dot or not.