I think this *would* have to do with GDPR, if indeed it took place. The data in question would be, presumably, emails and names of Labour members. Under GDPR that effectively belongs not to the Labour Party but to the people whose emails they are, and only people with permission to use or share them can do so. As far as I can sensibly see, anyone who left the Labour Party would instantly have to re-apply for permission to use and distribute the emails.
Now, I might be wrong, of course. But that basically leaves three options: this happened, and one or more of the leaving Labour MPs has been careless; this happened, and one or more of the leaving MPs has been deliberately criminal under EU data regulations to cynically give their new grouping a kick-start; or no data has been misused and, while the Labour Party is right to put these safeguards in place, you have to question the motives of publicising it.
I'm rather inclined to believe the third option, at the moment: it's been hard not to notice just how vicious and aggressive the far left wing of the Labour Party have been in trying to dig up, or create, whatever dirt they can on the "Gang of Seven", and this could just be another angle of attack to smear them before they become too much of a threat.