Karin is not Minato
Just as Karin is not Kakashi
Naruto
Bee
Orochimaru
Even Sasuke
and the rest
All of them had really no answer about not fighting him without looking into his eyes.
The same goes for Minato. He never fought genjutsu user. Why? because once trapped into it is basically game over for him if that jutsu is powerful enough. That's right if that jutsu is tsukoyomi Minato can't overcome it.
Minato needs his toads which doesn't even exist.
Canon is something we have seen in it in the manga.
I know X is not Y. The example was that if someone who wasn't bragged about his intelligence, was able to understand the mechanics of a jutsu, someone who was always bragged about it, called genius multiple times, should be more than perfect in understanding how some basics of a jutsu work.
And that is Minato.
Naruto is Naruto... we know that at that time, he had little to no info about it. As well, Uchihas were exterminated when he was born. So, little to no info about how to do it. Whereas in Minato's time, Uchihas still existed.
Bee wanted to fight that way, he acted all cool and stuff. However, Bee wasn't praised with intelligence and understanding the mechanics of a jutsu like Minato was. And if I remember, when he said don't look into my eyes Bee said I know.
Orochimaru. The all-time debated one. Orochimaru didn't even intended to attack him back then. He was just wanting to get more info about it. He got into the genjutsu more willingly. Too bad he didn't expected that coming and underestimated Itachi. One does simply not do that. But neither with Minato.
Sasuke wanted to fight that way. Remember it was a fight between the eyes, between sharingan prowess.
So, before giving these examples, look at the context. They might look similar, but they don't match.
You can't apply what happened to every character to a character. Contexts were different. Not all characters have the same abilities, nor the same intelligence, etc.
They act differently than the characters you're trying to compare them to.
Usually people always think from 1 character perspective when they start a debate. Nothing more wrong.
When you put them in vs, look at both character overall characteristics, ask yourself what x could do if y attacks him, given his abilities, intellect, etc. Never put one above the another. Place them as equals and then start calculating, to say like this.
But if you start going like everyone does, most of the times, with the premise that your character wins because you only take into calculation his abilities and characteristics, without taking the other one's abilities, without looking into how the other acts, given certain situations, that's why you start with the wrong premise that your character wins and the other one can't win.
Same thing Minato fans to when "countering".
In order to have a good debate, you must always, always take both characters into consideration, their abilities, intelligence, behavior in a context of a battle, but observing that battle.
It's not because Itachi has genjutsu that he can win, neither because Minato has FTG. Nothing more wrong!
Between these two, it's a battle of intelligence, brains, more than techniques.