For the record most women in Japan dislike a lot of the stuff that happens in Shonen anime as well. Mina Le gives a great breakdown about the school girl uniform and what's really going on there and how a lot of this stuff came about.
I would think it's better to frame this question as "Is Young Adult/Teen age fictional animation in Japan more problematic than Young Adult/Teenage fictional live action dramas in US/CAN/EU/AUS?" than how it's being framed here.
But to answer the question, no it's not more problematic because they both have problematic issues.
Firstly most, if not all of, Anime that comes to the west is drastically works that are written by authors that are writing for a young audience of teenagers. Shows like One Piece, or Dragon Ball, or BNH, or Bleach, etc. are all written traditionally for teen boys ages 10 to 15 or 16. Though it can be read by anyone, and it is. The idea is that the writers are writing to a younger teen audience who tends to think of dumb teen things. It's not designed to be read by adults as there are more mature comics that are written for the adult audiences out there.Series like Monster, or JJBA (the newer chapters) are all designed for older teens to college age readers that, while they may feature some sex, the way it's used is no where the same as what's shown in some shonen anime.
Also it depends on the writer and the editorial team. If you look at the works of say Blue Exorcist and D-Gray Man, neither uses the tropes that are typically seen in shonen works regarding how girls are shown in them, and that's partly because they are written by women. Series like Claymore or even Kenshin (Yes I know about the author) have, for the most part, zero to very little in the way of the tropes being used. Honestly I can't think of a moment in Kenshin where anyone touched the leading lady in a tropey manner.
Then there's the fact that these tropes are not prevalent in Shojo, or teen girls manga, which again is designed for teen girls, but they have there own issues that come with romance genres.
Second, there are a lot of anime in Japan that are no were as bad as the shonen manga adaptions that just don't show up here in the states. Some series are not easy to adapt to make them mainstream here so shows are passed on. The ones we get here are just the tip of the ice burg.So it's really hard to judge the whole of anime when really most westerners only see a very limited subset that is considered easily consumable here in the west from Japan.
Third teen shows and even teen media have always been problematic because of how drama's are made in the west. Right off the top of my head I can think of three series where you have the teen leads having relations with teachers Dawson's Creek (Pacey and his English teacher), Riverdale (Archie and Grundy) and Pretty little Liars. You see a lot of the tropes that Anime does in teen series in western teen dramas. Riverdale had Betty and Veronica kiss to titillate the audience.There are book series for YA where characters are basically teens having relations with older people or really young bodice rippers.Too many teen shows have moments of shots where you have the girls showing off their asses or their boobs in some way to the camera to make boys and girls (in regard to the guys taking off their shirts) get all hot and bothered with what they see.
So honestly if we're going to be judging these shows we have to have more context in regard to why certain forms of sexuality should not be explored or shown to teens.
Lastly, in regard to the whole Shesshomaru issue with Rin, I'd like to point out that Western books have done this before. Charles Dickens Bleak house has it where the lead nearly marries her guardian, and it's only at the end of the story that she ends up not marrying the man and marries her friend. There's other examples out there as well. Rin was 19 at the time she gave birth to the two leads in Yashahime, and the dynamic between her and Sesshomaru is that of a daimyo and one of the ladies of his court. There is no father daughter relationship, that is with Jaken. The point of the story is that of a fairy-tale, and, as with Tales of Genji, for example, this follows a lot of actual history for nobles of the period.
If you want to get down to brass tacks, Date Masumune married his wife Megohime when she was 12 and he was 15 and she had their first kid at around 14 or 15 years old. The fact that they have Rin as 19 makes sense within the time frame of the story and the history of the period. Is it weird to us in the modern era, sure, but it doesn't change the fact that culturally in that time period women had children young because children had a higher mortality rate than they do now. And teenagers and kids only really started to be treated a lot like how we treat them now during the later 19 and into the 20th centuries. Before then, teens were considered young adults.
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