Shipping. She actually does come in the way of the ship because Inuyasha does love her too. Kagome is more relatable than her. Even the way Kikyo was brought up is just not something a lot of readers can relate to. Personally I find her a fascinating character. There should be more female characters that aren't moefied and sexualized to death while still having that "cool" personality. It would also be nice if people could look at Kikyo and Kagome's characters and realize they come from totally different backgrounds. I don't hate either of them.
Sakura hate on the other hand is not due to "coming between a ship" because neither Sasuke or Naruto care about her enough. Naruto and Sakura don't even interact much anymore, and Sasuke literally react like this when he saw her after many years;
And he never kissed her in canon.
The reasons people dislike Sakura are:
a) she wastes most of the screentime and many important situations she's in (which is a lot compared to many other characters) by being useless
b) she treats naruto poorly yet naruto is the one who has to save her ass all the time, and if not him then kakashi, yamato, you name it
c) she treats sasuke like an object, she doesn't care to listen to him at all, and acts like a victim because sasuke isn't romantically interested in her
d) she treats other women who help her poorly
As for me I dislike her fanbase more than her. They are insufferable and toxic, and can't accept the fact she's just not an amazing role model, badass or a likeable character in canon. They call you a misogynist for disliking her canon manga character, but then change her character into something different in fanon. Not to mention they always blame other characters for her failures.