I know a lot of Christians who like it. I used to watch a lot of anime over a decade ago. Some of them have decent themes, but one of the things that weirds me out is the apparent hyper-sexualization of female characters, many of which are clearly not adults (Many anime shows take place at high schools or with high school aged children). The well-known idea of "fan service" in these shows and films is enough for me to find it unnecessary to watch. Others I have talked to take issue with the excessive gore/violence. Obviously not all Anime shows have fan service or excessive violence, but I would dare to say that most of them have at least one of the two. I don't really watch TV any more, I cancelled Netflix and Hulu a long time ago and haven't had cable since I moved out of my parents house at 18, so I have to go out of my way to watch TV in the first place. What I'm seeing in this thread are two main critiques, the first being that TV in itself is kind of waste of time, and the second that the community of people who watch Anime is, well, interesting. I'll add my critique to the pile that many of these shows are kind of degenerate. If anybody remembers the whole "Should Christians watch Game of Thrones" debate a while back, I imagine we're going to find many of the same talking points in this discussion.
All that said, I don't find many of pro-anime arguments compelling because they often seem like the same justifications people use to do anything they know they shouldn't be doing. Just because somebody can divine a gospel theme from between the lines of a piece of media doesn't mean that the piece of media is wholesome or worth spending time watching. I'd rather somebody just say, "I enjoy anime" rather than hyper-christianize the argument by saying, "Well I watch it because of the Gospel themes." Just because something has Gospel themes doesn't mean that the piece of media is worth our time. There are tons of movies that have redemptive themes and also are borderline pornographic, vulgar, and not wholesome. If the argument is, "I watch Anime because of redemptive storytelling," I can point you to a book that is full of that kind of content. In short, if you're watching something solely for the reason that it has Gospel themes, it seems more productive to just read the Bible, or enjoy a work of fiction that is by design a gospel allegory rather than trying to scrape Gospel themes from animated shows that are clearly not attempting to be Christian media. I'm not particularly convinced of the whole thought that Christians should only watch media that is intentionally Christian, I'm just saying that it's not a good reason to consume content just because you can interpret Gospel themes from it.
The second critique that I saw in this thread has to do with the community of people who watch Anime. I have found that this genre attracts many people on the spectrum, which isn't a problem, but I have personally seen friends of mine with ASD learning to socialize from Anime and the result is maladaptive. If you have watched Anime, you will know that the social dynamics between men and women in these shows are unrealistic and intentionally...not realistic and will have the result of creeping people out or making people feel uncomfortable. I have also seen it serve as a gateway to certain types of adult content which malforms the mind and is very unhealthy. I'm not saying that Anime is a gateway to animated p0rnography in every case, but it certainly can be and has been for some men that I have talked to and counseled. I know a handful of men who I have helped with p0rn addiction who found animated p0rnography and justified watching it because "It's not real people." Some of them credited the "fan service" of animes they watched as the reason they got into this genre of p0rnography. Obviously I'm not saying that Anime leads to p0rn, but we all know how men think, and we at the very least should be aware of the risks of watching over-sexualized content in any medium (i.e. Game of Thrones).
In short, I don't watch Anime, or much of anything for that matter, and I don't find the argument that "Anime has redemptive components in it" to be particularly compelling as a justification to watch it. It is okay to watch something on the sole grounds that it is entertaining and well made. I'd rather somebody make an argument for a specific animated show on the grounds that it is a great piece of media than on the grounds that "it's basically a Christian story". If we're being honest with ourselves, most anime is not intended to be "christian media", so if that's your argument, it's not convincing. If I were a big media consumer, I personally wouldn't spend too much time watching Anime due to my aforementioned critiques (fan service, excessive gore, etc.). I know there are wholesome anime shows out there, but I would suggest that people be aware of the degenerate themes that exist in many of these shows and to shield your eyes and ears from anything that might lead you down the path of p0rnography, which is an epidemic among men in churches. Also, why watch anime when Turretin exists (mostly kidding, but come on, Turretin!).