Just because it's obvious to the viewer that a character is madly in love doesn't mean that it is for the characters. Actually, there are plenty of characters who are completely oblivious to the fact that someone has a crush on them.
Sometimes, it's understandable that they wouldn't get it - Violet Evergarden is a child soldier who doesn't understand human emotion in general, so of course, she's not going to get even the most blatant of confessions. But at other times it's just kind of ridiculous - how in the heck does Tanaka of Ueno-san wa Bukiyō manage to miss all of his senpai's clear signs?
Whether it makes sense or it doesn't, these clueless anime characters can be entertaining, but they can also add some serious drama to the stories they're involved in. Which one is the most blatantly oblivious? That's for you to decide.
Umetarou Nozaki - Monthly Girls Nozaki-kun
Being completely blind to someone else's romantic feelings is actually the main theme of Monthly Girls Nozaki-kun. Umetarou Nozaki somehow takes Chiyo Sakura's explicit confession of love to mean that she's a fan of his shojo manga and wants to be his art assistant. Chiyo spends a huge chunk of the series attempting to get Nozaki to understand her actual feelings, but no matter what she says or does, he remains completely clueless - ironic for someone whose job involves depicting matters of the heart.
Hinata spends years nursing a huge crush on Naruto, but he's far too preoccupied with his quest to retrieve Sasuke, his crush on Sakura, and his various ninja missions to notice her. It takes until a post-series movie - which takes place years after they first met - for them to finally get together - and by that point, Hinata has made her feelings pretty clear. Not only did she do things like give him medicinal ointment and other gifts during the early days of their friendship, but she also defends him from enemy ninja and basically declares her love for him during Shippuden.
Naruto still manages not to get it - though it's possible that he just doesn't want to deal with it until he's prepared with some kind of answer and not busy trying to prevent the end of the world.
Violet Evergarden - Violet Evergarden
The entire plot of Violet Evergarden revolves around the titular character's inability to understand love. When she worked as a soldier, she worked under her major, who told her that he loved her before passing away. She doesn't understand what he meant by that, and she thinks that if she has a job that helps her understand human emotions, she might gain some insight. To accomplish this, Violet takes a job as an Auto Memories Doll, a job that requires her to write emotionally nuanced letters that depict the inner feelings of her clients.
At first, she takes everything literally, mangling her letters and failing to notice when the people she meets having romantic feelings toward her or toward anyone else - but as the series progresses, her emotional intelligence grows.
Kousei Arima - Your Lie In April
When you're heavily focused on your own personal issues, it can be hard to notice that someone else has feelings for you. This is definitely the case for Kousei Arima. While it's blatantly obvious to the audience that both his childhood friend Tsubaki and his fellow musician Kaori are head over heels for him, he doesn't notice Tsubaki's feelings and he easily believes Kaori's lie that she's interested in someone else.
To be fair to Kousei, Kaori is actively trying to conceal her feelings toward him, but her passionate interest in having him play music with her could have clued him in. Sadly, though, he doesn't realize how she feels about him - or how he feels about her - until she's passed away and it's too late to do anything about it.