Huh. Well, a quick wiki walk has taught me absolutely nothing about Minsc post-Bhaalspawn crisis. But I did learn that Bioware's in-house DnD campaign was set in
Dark Sun and that Minsc was a character from that.
I'm sure not going to tell you that you're wrong about how you feel. But I don't think the original Baldur's Gate games have anything in common in terms of theme or feel. The original is a very open ended campaign where you're scrabbling for clues about who killed Gorion and why. It's linear, and you're always going to get to the same place in the same way, and I'd call it a personal story but it's pretty barebones until the last two chapters. Being set on the Sword Coast, it's about traveling from place to place, getting lost between the city-states.
The second game is very goal-oriented, but it's not really about you--it's about Irenicus. While it's much more character-focused, your character specifically is tangential to the story; you're a subject of the plot(s), and a plot device. There are a few different ways to get to where you're going, but little freeform exploration. In exchange, the places you visit are denser, and quite a bit darker--Amn is one of the Lands of Intrigue and it shows. Most of the characters from the first game come back to variously be disposed of, rejoin the party, or do their own thing.
And then Throne of Bhaal. Your main character is the focus again since it turns out that the prophecy of destruction from the first game is what happens if you fail (or embrace it). It's the least grounded given that, and deals entirely with epic level subject matter, like stopping a war singlehandedly, a True Resurrection, killing immortals, and of course the godly portfolio up for grabs. Discounting Watcher's Keep you're basically on the critical path the whole time, since the sidequests are almost entirely things you do along the way to fight the next member of the Five.
Looking at it like this, I think you could easily convince someone that the games weren't connected if you leave out the part where you're (optionally!) playing the same character. Especially since you're not IN Baldur's Gate for 95% of the series, and it's a legacy title by Tales of the Sword Coast. And that's why I'm not concerned about BG3 not being thematically identical--the original trilogy wasn't! Heck, it actually has the most in common with Mask of the Betrayer, which happens to be my favorite PC game.
Art-wise, sure there's nothing here that looks like the BGT... but Pillars of Eternity did and I ended up loathing PoE for being a soulless clone of something real. Which is on-brand at least.
That was the Cult of the Unseeing Eye--so, undead/blind beholders. The illithids were in the Underdark segment. I'll be pleasantly surprised if we do see more than references to the trilogy, but I almost hope they decide to push the setting forward rather than look back.