I don’t really understand why so many people are so opposed to the idea that they’d drop the series altogether.
The only argument I can think of is that Smash is a crossover fighter and characters from outside gaming wouldn’t fit. The problem is that we’ve had other crossover fighters with guest characters from outside those properties already. Like the TMNT were in Injustice and Pac-Man was in Street Fighter vs Tekken.
Depends what you see Smash as. These days it's mostly seen as a confluence of gaming (though it hardly takes evenly from across the industry), so anything outside those parameters clashes with the identity it's been given.
"Nintendo purists" get derided, but for a while Smash was a crossover purely of Nintendo characters, so when that changed, they had dissonance between what they saw Smash as, perhaps what they valued it for, and what it became. I like the third-party presence, but I understand why some people lamented the shift, if they considered Smash something apart from what it turned into, much as many would lament if it opened its doors further.
And then there are those who have a more "this is just a big crossover, and it'd be cool if they added x" approach - and therein you'd see the Gokus and the Batmans and the Spongebobs suggested. That's not where I stand, and I wouldn't be thrilled if that's what Smash became, but... it's not impossible it one day goes down that route. Especially once Sakurai fully departs the series, and they might be looking for a new hook.
If people are so concerned with preserving Smash’s original identity, why didn’t you stop playing when Snake was revealed in Brawl? I just don’t get it.
It's possible some people did, but it's likelier people who weren't happy just complained and then gradually got accustomed to it, and then eventually stopped. I mean, if you still have a problem with it twenty years later, you'd either have left or by now would just keep it to yourself.
The truth is though that what happened then would happen again if we got non-gaming characters, being a blowback that eventually subsides as people accept the new direction and while some may pull away, a lot eventually embrace whatever the series becomes, and non-gaming characters begin to show up on popularity polls and the like.
It wouldn't be new. Past third-parties in general, there used to be an aversion to fighting game characters in Smash until Ryu showed up. Lord knows about the aversion to non-Nintendo-oriented characters, and now most of the most requested third-parties aren't heavily Nintendo-oriented.
The fanbase will just adapt to whatever the direction is, and that includes if they added non-gaming characters. Not to say there wouldn't be blowback and the fanbase doing a lot of fighting with itself before things smoothed out. Snake only truly stopped being divisive around the time of Cloud and Bayo.
Plenty of other fighting games have had guest characters from outside gaming. For example, Soul Calibur had Darth Vader, Mortal Kombat had Predator, King of Fighters had WWE wrestlers, and Tekken had Negan. What’s so different about Smash where it would tarnish the spirit of the series but it’s fine for these other games?
These other series you mention, apart from sort of KoF, have guests but aren't intrinsically crossover series, and never established themselves on the basis of a particular medium of guest list. In fact, I believe both SC and MK's first guests weren't game characters (well, one of SC's first three, being Spawn).
Those series have different sorts of identities, such that people generally see medieval-themed weapon-wielding characters as those that would fit best with SC (hence why characters like Link, Marth, Ezio, a Soulsborne character, and Kratos - though he's not medieval) are/were popular requests. And why even though it got Star Wars, that was seen as... weird. A character like Mario wouldn't fit in SC, outside of character creator at least, because it's even further from its identity. And with MK, generally characters with over-the-top violent backgrounds (such as movie slashers or comic villains) are among the most "fitting", as they are in line with the series' identity.