Morality is always a tricky thing in roleplaying games, I guess.
There are people of who have no problem playing an Evil Campaign in D&D where they will be the baddies who steal, kill, pillage, destroy the world.
In CoC case it's a bit harder because of the serious tone of the game (Well, except if the keeper decide to run a more "lighthearted" campaign, I suppose...). Being in the shoes of mobsters, cultists, or any other kind of assholes in this game is supposed to affect the players more than, say, if a group of D&D players decide to play a bunch of goblins who are attacking a village to steal stuff.
In my case, I wouldn't make my players be completly evil characters (Except if they ask for it). I'd rather run a campaign with greyish morality. As someone said before, in a "normal" campaign, the investigators might do bad things and they might appear as a group of maniacs killing people and destroying building for no reason.
I would offer my players choices they won't be proud of. Hard decisions. Uncertainty.
It's kind of already the case in the campaign I'm running : During their second adventure they discovered that a cunning woman has been kidnapping babies for months, maybe years. She used them as sacrifices during rituals performed to maintain a barrier which has been preventing something from destroying the whole region. The barrier was getting weaker and weaker and the woman became desperate. (And it affects her very much)
She wasn't evil, I mean not "I will destroy the world" evil. She was actually trying to help but was forced to do horrible things for that reason.
So I gave my players that ambiguous situation. Will they let the woman continue her awful deeds and hope that it will work? Will they stop her?
In the end, the investigators found an alternative solution (Something the woman was aware of but couldn't pull off alone) and the woman turned herself in to the local police.
Besides, I have in store a little adventure who could totally end up with the investigators being forced to let go a potential serial killer (Because they can't just tell everyone he is a killer for they have no proof against him and he's too powerful) or they could simply kill the guy. (And during this adventure they will be in contact with the local irish mobsters so...)
So, would I let my player be part of an evil organisation or help such an group? Probably, but with a lot of ambiguity. Maybe they will be german soldiers who will be deeply affected by the horrors commited by the Nazis. Maybe they will be given the opportunity to use the ressources of the KKK to stop some cultists (Classic "The enemy of my enemy is my friend"). Maybe they will have the choice of killing or letting go an assassin that just helped them.
And about the fact that any hard choice becomes meaningless in the great scheme of things because the very nature of Cosmic Horror is that Man can't do **** to prevent the Apocalypse, I'd say it's a matter of perspective.
Normally, the investigators are not aware of that. That's when they realise that what they do is meaningless that the true horror begins to take them over. Otherwise, when they decide to take extreme measures to stop a cult or something like that, they don't know that Cthulhu, Nyarly & company will come to Earth one day anyway.
It's the bittersweet nature of Cosmic Horror. See Stranger Things 2.