Well, he was just regaining consciousness, but again, he was only regaining consciousness so he probably wouldn't have been seeing all that clearly, and besides which, she was directly in front of the sun, which would have distorted her colors somewhat.

Wasn't he passed out when she sang to him? And he heard her voice, but did not see her in person? Sorry if this is a dumb question.
Nirvana, Pearl Jam, Soundgarden, Alice In Chains, and My Little Pony: Friendships Is Magic fan

Not to mention Ariel was directly in front of the sun when he saw her, so elements of her appearance would be dullened. And besides, he DID in fact recognize Ariel and even immediately assumed she was the one who saved his life when he encountered her later. In fact, the only reason he decided otherwise was because he then discovered that she couldn't even talk at all, which is an understandable reason for assuming she couldn't have been the one (not to mention he was disappointed when he thought she couldn't have been the one after that).

I don't think he took the vision all that seriously

It would be pretty hard to pay attention to her hair color when she's literally in front of the sun when he woke up. Heck, when we see his POV when he sees Ariel, because of how she was in front of the sun, her hair DID appear dark brown.

I guess so as he must never paid attention at all to her hair color

Also in stage adaptations there is some variation
In a NON Broadway version Ursula killed Ariel's mother
For all those who claim Ariel does not learn anything she acknowledges her actions mistakes at plays's end though to all the cynics it means nothing
I should mention in that version NO Heely's NO elaborate sets
AND YET they put together a Damm good show some ways surpassing the Broadway show
and that's my two cents

She would have, had Sherie Rene Scott not nixed the idea due to the song "All Good Things Must End" due to it conflicting with her vision of Ursula.
And anyways, the sun was literally in Eric's eyes, he was just regaining consciousness, and considering Ariel was pretty much eclipsing the sun, any red in her hair would have been drowned out (in fact, we actually SEE Ariel from his point of view when he woke up, and we didn't even see any red hair, and in fact, her skin looked darker than usual). For all he knew, she could have been brunette, so I think I could forgive him for not knowing she was a redhead.
One last thing, he DID in fact instantly think Ariel was the one who saved his life when he not only recognized her, but she in turn confirmed they've met before. The only reason he decided she couldn't have been the one was because it turned out she couldn't speak at all, let alone sing to him, and he was disappointed by that discovery. And as far as Vanessa, he was brainwashed, remember?

Ariel was in a golden haze from the sun (Also Film Noir there) so he could not see her that well BUT THE VOICE
Also Ursula/Vanessa used Ariel's voice to put Eric under a spell hence
In the Broadway adaptation Grimsby suggests that every maiden in the kingdom comes to the castle to sing for Eric thus he will find the mystery maiden
Mute Ariel tries and obviously can not get his attention thus when the sun sets Ursula claims Ariel
She does not turn into Vanessa in the Broadway show