Under the old TV system people would find out one by one the secret identity... Now with Supergirl they just skip the new person each season and have a few of them find out right away. I actually think the Supergirl solution is more realistic. Not having your hair up in a bun without glasses is a disguise for anyone that is with you everyday? Her boss "Cat" is barely believable not recognizing her, just makes her look really narcissistic and not even bothering to really notice her underlings.
Really Lois Lane super in love with superman, with all sorts of close encounters, yet working every day with Clark Kent is fooled for any length of time?
I thought in the superman movies back in the 80's, it wasn't just the glasses or hairdo made him unrecognizable. It was a super power that does that. So this is not the case with Supergirl? All they have to do is put supergirl pic on facebook or google photos and her secret identity will be found.
I was search for my son's picture the other day on google photos backup.. and it found him in a picture of 20 of this classmates. I am very impressed with the facial recognition.