I call bullshit on this. Most of the outrage seems to have been stirred up by Thomas Hawk, who happens to be the CEO of Flickr’s major competitor.
The change has absolutely no visible effect. I switched to using my Yahoo ID long ago and it didn’t affect anything. You don’t even have to use a Yahoo email address – I still use my gmail address. My visible user name & photo URL remains the same. It didn’t affect my pro status. You’re the only one who knows that you’re logging in with a Yahoo ID – everyone else sees exactly the same thing they saw when you logged in with a Flickr ID. It simply means I have one less password to remember.