In my previous life, we had some 568A and some 568B, depending on who did the cabling—our telecom guys used one standard and the AV contractors used the other, though I can’t recall which one used which. For networking, it doesn’t actually matter which one you use as long as both ends are terminated the same. If you look at modern Cat5E or Cat6 keystone jacks, you’ll see that they show the color codes for both A and B on the punchdown blocks.There was a T568A protocol that AT&T used but it wasn't the accepted standard.
FWIW, that’s not old school phone cabling in the picture, it’s Cat5E network cable (it says so right on the sheath). It’s good for network speeds up to 1Gbps, although it was supplanted by Cat6 over 20 years ago.