I've had a look at that Reddit thread. I am gently bemused by what seems to be the emerging TRA consensus, which is that the dog is NOT reacting to the wife's natal sex, but to the "fact" that she is must just be a terrible dog handler with awful training techniques. (Based on no info other than the dog's reaction, of course.)
I probably shouldn't be surprised, but isn't it interesting that it's more acceptable to be told that you've screwed up (ie how you trained/handled the dog), rather than that the dog doesn't recognise your non-physical identity.