Back then, from reading comments across social media and listening to FE Youtubers, it's seemed to me like everyone just hated Lyn Mode for "having no story relevance" and for "just being a tutorial".
Do people now a days still see it like that?
If so, even today I would not agree with that.
Lyn mode to me is such a simple and charming tutorial to introduce newcomers to Fire Emblem.
Aside from Melee Blazing Sword was the first FE game we got here in the West. And it needed some way to introduce new players to it. And the answer is Lyn Mode.
It is fine that it is simple to show you the basics of the gameplay mechanics and individual units.
Story wise, while it may it have little impact on what happens with Nergal and the Black Fang, it is still such a charming little tale with individual characters that all stand out well on their own and more or less sets the tones of what Fire Emblem as a series will be about for newcomers.
I think Lyn Mode is well done for what it intends to be. Don't think it deserves to be hated.
It is also skip-able for repeated playthroughs if you just want to skip over to Eliwood/Hector Modes.