Can't see that this is anything to do with GDPR, this is nearly all historical stuff. Now, if they removed the UK Electoral Rolls 2002 - 2014 from the site, that might be GDPR - that makes modern people identifiable. Except that since it's already online, the advice seems to be that that's OK - apparently names and addresses in old parish magazines are not seen as a problem either, but that going forward, permission to put stuff like that in magazines has to be obtained in writing.
Seems you can do what you like with data - as long as the subjects have agreed beforehand. Companies House displays full names, addresses (although you can use a company office to disguise that), and year and month of birth, online, and tell us it's because it's a public register, that they have to do so. My name, address and phone number are also on display on the Charity Commission website, as contact for a charity I'm a trustee of.
No, I think this has far more to do with money than GDPR.
All that's useful about My Records for me is that little black tick that tells me I've already seen that one! If I really want it, I take a copy, just like I would at a Record Office. Otherwise I'm really not interested.