That's a good point. If I don't mind that Barry doesn't have blonde hair on the CW Flash show, doesn't mean I should be cool with whatever is changed about another character that I might feel more attached to, compared to The Flash.
Also, what you said earlier that it's ok to want a white character to be played a white actor, I think it depends on the way fans express themselves about it. If they are all nerd raging and insulting the actor and the filmmakers, then it comes off as embarrassing, ignorant and completely out of touch. But if they express themselves in a proper and more logical manner, then even if people on the opposite side still disagree with them, they can probably at least gain some level of understanding towards where they're coming from.
I'd give a random example with Green Lantern Kyle Rayner. When Kyle was first introduced in '94, he was originally depicted as Caucasian and there was pretty much no reason to believe otherwise. He was drawn as a young white male with black hair. Then some years down the line he was given a Mexican-American father, so nowadays Kyle is naturally considered to be Latino and he is therefore drawn to look more that way. Yet, the character is still at times drawn to look white as well, in his appearances in the DCAU he also looked white and if you don't know this detail about his background, you may very well not guess that he is supposed to be Latino right away. If Hollywood for some reason decides to cast a white actor for him, I personally wouldn't see it as whitewashing because Kyle was not originally created as a minority character. The same way not many people probably know that Hal Jordan is Jewish, because that's not something that's been accentuated on too often and hasn't played a big part in his history. Same thing, I would be totally ok if Hal isn't played by a Jewish actor in the DCEU.
People may naturally disagree about all of this and insist that Kyle absolutely must be Latino in a live-action movie and that this time Hal needs to be played by a Jewish actor, but they'd at least know where I'm coming from and I won't be just spewing hatred towards a casting choice solely based on their ethnicity. To be honest, I think both sides of the equation need to show more understanding towards one another whenever a casting choice like this happens.