I don't think I agree that Kara was in the right -- or at least, I think she and Alex had equally valid positions -- but the real issue wasn't what Kara was arguing, but how she argued it, by getting pushy and not deferring to Alex's authority about her own daughter. That was overstepping regardless of the merits of her position.
"Its not how it was like when you were young" said Alex about racist anti Alien beliefs.
Superman probably saved the world from many alien invasions, that killed millions(?) of people.
So many Space Hitlers.
Of course the little alien girl had to hide at the turn of the century.
Society is more nuanced now.
Cough - Ben Lockwood - cough!
Society can see that not all aliens are to blame for all alien aggression against Earth.
Kara is right to hide from murderous lynchings. She's still hiding so long as she has a secret identity. Although did Supergirl murder Kara Danvers last week? Kara Zor-El is a real person, but Kara Danvers might be toast.
As a Gay woman, Alex wants to confront and diffuse the mob, and become accepted, even if Esme's Kindergarten is the new Stonewall. Alex has been an out gay woman for 5 minutes, but she has a gun, a badge and combat training. Alex had the benefit of hiding who she was for decades, to create a hetero normative accepted life where she could thrive as a person who does not have sex with any one compatible.
If Alex had come out as a teenager, and Hank Henshaw was never replaced by the Martian Manhunter, it's likely that she never would have risen to a position of authority in the DEO. She would have been a punch line hidden in a closet sized office never given the same opportunities as a straight woman.
Living a lie for all those years, is why she doesn't want Esme to live a lie.
