I can see that there is aim assist setting even in MP, so what's the situation with that?
Console versions have a suite of high value aim assists. A short step away from aimbot, imo.
Isn't it bad to play with aim assist disabled against someone who has it enabled?
Absolutely. You will be putting yourself at a HUGE disadvantage.
Is that aim assist subtle and actually a thing of preference, or just a bad game design choice?
Excessive not subtle, and leads to balancing issues. The only reason I can think of, as to why the aim assist is so strong, is probably to level the playing field and sell more copies.
Is there a way to filter servers and play with players with same settings? Are there any modes that disable aim assist for everyone (hardcore or something)? Should I even bother with all that?
You can turn off the aim assist for yourself, and that's it. "Hardcore" does nothing but reduce your health to 30%, and remove HUD elements (including the crosshair, lol.)
Any general advice for a new console cod player coming from pc? I disabled aim assist right away, but should I continue playing like this, does it make sense at all? I woulld certainly enjoy playing without any aim assist in any game, but this situation is little wierd, as it affects MP game at the core.
Turn aim assists back on, absolutely. Unless you enjoy the challenge, and don't mind that everyone else has a HUGE advantage on you. Watch the killcams - notice how people's crosshairs "snap" onto targets, across a surprising distance. Tonight in fact, I had to fight my controls to stop pulling my crosshairs into a rock, where an opponent was hiding behind.
Besides this dilemma, I'm really enjoying new COD experience on a console, I'm new to it and it is refreshing to me by itself. I'm tired of over decade and a half of M/K in mp, every game started to feel the same to me, so I want to try something new.
There are M/K adapters out there for consoles. CoD works very well with them.
XIMs probably being the best ones, with 1:1 mouse movement.
If you like CoD, I'd recommend giving HALO4 a try. Halo games feel really good with the controller. Each weapon has a distinctive feel with the rumble pad. That's my recollection of Halo:CE, anyway.