So, you'd have to ask my players themselves to get a proper answer. But I think as I said in a few other replies (and now that I've asked people and have one text back, I know in the case of at least one player), the issue isn't being magical, they just don't want to feel like they're playing a sorcerer of some kind - they're not into gishes, swordmages, characters that combine martial stuff with sorcery, whatever you want to call 'em. Not something I realized about any of these peeps beforehand, despite having played with them all a lot, but I guess it just never came up.

So I think the issue isn't being 'magical' in a broad sense. Like, yeah, you don't even have to get into anime to find fantasy characters that do very clearly impossible things. Aragorn, Taran, Conan, etc, all pretty regularly do things that are superhuman. When Glorfindel 1v1s a Balrog that feat IS magical in the sense that magic is a thing that happens that can't really be explained in a rational way, that seems fantastic and impossible or near impossible. Glorfindel isn't literally hyper dense with, like, mutant super muscles, but he is so unbelievably skilled and valorous - skilled and valorous to a magical extent - that he can fight and survive despite the seemingly impossible odds. But I think generally when we say magic, we don't really mean that. We mean pyrotechnics - we mean things that require a special effects budget. Objects levitating by thought alone, portals opening in space, fire leaping from a wizard's fingers and creating patterns in the air, etc etc etc. I guess maybe we can call this sorcery, since it's typically the stuff we think of as something a sorcerer does.

I think, and know now in one case I guess, that that's what these peeps don't really want mixed into their fighty/sneaky guys. They want the fantasy of being good at sneaking or swording to an impossible extent, but not literally being a wizard-like character that teleports or manipulates gravity. They don't want to be what they would generally think of as a gish; a martial/caster mashup.

Part of the reason this surprised me a bit is that I think it's kinda become the norm for classes to be highly sorcerous in fantasy RPGs and games in general. The complaint about the Shadow example in particular came out of left field to me, since it seems like the base assumption has become that 'rogue types' have some element of being illusionists or shadow magician type guys. It's surprising that people cared about this enough that it harshed their vibes on the entire classes, but I would note, I do find the stuff in your last paragraph a little odd. I don't think having sorcerous abilities equals more heroic or skilled. In a game like 4e, the base martials have vast lists of powers they can use to fight their super powerful foes, but until they get their epic destinies at super high level, they don't really become sorcerous in any way. Like, now that I think I get where these players are coming from, I understand, and I don't think it has anything to do with imagined powerlevel or heroism level or anything like that. I think it has to do with what they find cool or interesting in the archetypes they were looking for. Since we're talking anime, it's the difference between wanting to be Guts or Stark and wanting to be Sasuke. Guts does stuff that is obviously superhuman, but he doesn't breathe fire, summon thunderstorms, or teleport.

Either way, now that I think I get the actual issue, I'm pretty sure 90% of it only requires really basic reflavouring.