For me it's solely down to how much a character means to me personally. So, I want a dark haired Batman, a dark haired Superman, a dark haired Wonder Woman, a blonde Supergirl, a blonde Power Girl (one day?), and a blonde Harley Quinn. Aquaman was never a character that meant much to me so it doesn't bother me that they changed his hair colour. And Momoa rocked it. Likewise, I've never been a huge Flash fan, so that change doesn't bother me. The more the character means to me, the more I want to see what's on the page up there on the screen.
Yep. I'm with you. This is basically my attitude towards these changes, too.
The more I'm a fan of that character, and the more attachment I have towards that character, the more resistant I am towards changes to that character.
I'm a fan of Supergirl and she's probably my favorite female superhero. I'm also a fan of Raven from Teen Titans. Yet, those characters have completely different looks and personalities. I would not want a Supergirl who looks (and acts) more like Raven nor a Raven who looks and acts more like Supergirl. Otherwise, they'd become completely different characters!
These characters were created with a specific visual design. And for comic book characters especially, that visual design is a big part of their identity. It's partly what attracts us to the character in the first place and maintaining a consistent familiar design is partly what keeps us hooked on the character throughout the years.
For example, Superman is by far my favorite hero. But, if I he looked and acted more like Lobo, I doubt I would be interested in the character. Or, if Supergirl were still a blonde but sported a mohawk and was covered in tattoos and piercings and trash-talked with a foul mouth. Again, I wouldn't be interested.
Granted, those are extreme deviations. But even something simple like changing hair color from blonde to brunette throws me off and makes the character less recognizable (to me) as that character.
When I see the manips of Sasha as dark hair Supergirl, I don't immediately see Kara Zor-El because that's not how Kara has always looked. I see "female Superman" or Superman's daughter or Lois as Superwoman. Even as an alternate universe Kara, it doesn't strike me immediately as Supergirl.
But, when I see the manips of Sasha as blonde hair Supergirl, I see Kara Zor-El. I recognize that character. When I see a blonde in a Superman looking costume, I immediately assume that's a version of Supergirl because I associate that particular visual identity with that character.
With all that being said, I'm willing to give Sasha a chance as Supergirl. But I'm going to withhold final judgement until I see what she actually looks like as the character in costume and until I find out more about her character's role.