I have now found the 'cause', if you want to call it that: IPv6.
If I disable IPv6 on my laptop, I can use these websites with no issues; when it is re-enabled, both sites give non-actionable error messages. I have been using the same /48 block for my home LAN for more than 14 years, and have never operated any systems on it which would cause it to have a 'bad reputation' (but it is an assignment from Hurricane Electric's Tunnelbroker service, so may have been aggregated with other blocks from that service). IPv6 to the remainder of the websites in question works just, only login is affected.
I can only assume that somehow the IPv6 address range I'm using has been 'blessed' by Google as unsafe or unsavory in some way.
#IPv6