There is an air of colorism just inherent to this story. In a lot of Asian countries there is a lot of colorism just baked into society (though the forms differ quite a bit between different Asian cultures). Even the comments by the other characters in the story why around seem very similar to how I've seen colorism being enforced societally in a different Asian culture. People will say it is for your health and maybe they are concerned about that as well, but will also say "health" because it is more societally acceptable to say those sorts of health comments. However their solutions do not make sense if you only look at it as a concern about her health [see pages 8-9 to see that the mc identified her own motivations related to what she sees as beautiful, but hides it under health comments]. In this case the colorist solutions of those around Keika, like to completely isolate from the sun, are stopping her from having a more healthy relationship with sun exposure. And in the end, she looks out for her own health by taking an umbrella with her, something that wasn't a solution to those around her because it would still involve her skin getting darker.
There's just some inherent shame and shaming of getting darker skin, that's from colorism. Though this story does seem to use colorism as more of a metaphor. It has clearly harmed Keika, keeping her isolated from the world, and I would argue that has harmed her more than any damage from the sun.
It's absolutely true that the protagonist exhibits colorism. What is much less clear is whether the story approves of her colorism. In the climax, Keika follows the protagonist's request to stay indoors (== get pale skin) as an apology, but the narrative equates this with death. So I think the most natural interpretation is that the protagonist's colorism is analogized to Keika's controlling parents and ultimately portrayed as a bad thing.
I also read the story as not portraying colorism as a positive belief.
However the colorism still does make me uncomfortable, mainly because I read it being used more as a metaphor the story uses rather than a rather pervasive and oppressive ideology. This leaves a bad aftertaste when colorism isn't a topic well discussed in media.