Oh dear, I use multiple clients so I'd better have a look and see if this could be a "thing".
So I login my main, no problem. I fire up a second client, no problems so far, it appears and I enter my login details. Then this appears:
Damn. That isn't good.
Reading further comments in the Reddit thread there was much mirth, laughing, finger pointing (they want us to only have one character), serious fraud possibility [tinfoilhat] the power of 2 promotion would be negated and thus they could be liable to fraud [/tinfoilhat].
Amongst the trolls there was a good fellow though and he pointed out a temporary fix:
It did indeed work but ....
as this was all going on CCP have released a new patch that fixes the issue, which it does, no word from CCP on this issue (that I can see) and the Reddit thread is CCP Falcon empty at this time (it is nearly lunch after all :)).
Tin Foil Hat
This should be a major embarrassment to CCP. Testing has missed something as such basic functionality as multiple clients before it was released. Unless of course this was done on purpose to gauge response from the community or for some other nefarious reason?