I think there's a big problem in recruiting companions, in a lot of the cases, your character would have to be downright stupid, or have some other very specific reason not to recruit many of the companions, this is because of how the story starts.
Right from the get-go, you're immediately thrown in a personal crisis situation, you're infected with a mindflayer parasite, and so are all of the potential companions you meet at the start, the both of you have very clearly the exact same goal, and an extremely urgent one at that, to deny their aid just because you have some sort of personal disdain for them or their morals is downright stupid.

Are you really going to deny help of Lae"zel because she's extremely aggressive? She appears the best lead by far to a cure to your situation, her people being very experienced with mindflayers.
Karlach is clearly not evil, and even if you're evil, this still means you can use her without fear of her stabbing you in the back unprovoked, same goes for Wyll.
Shadowheart reveals to be a Shar cultist, but again, that's sort of the least of your worries right now, compared to your predicament.
Only Gale and Astarion pose some sort of actual threat to you unprovoked, and even so, by the point you know of Gale's ailment, you know this situation is about more than just you.

I think Larian made a pretty big mistake by starting the game off with such a huge threat to your character, it would have been better to meet these companions before you knew just how deep the shit is that you're in, this way you have a realistic choice of either denying or accepting these companions, Lae'zel for example could have a hunch that the Mindflayers are behind this, but with how little you've seen about the situation, she might just come off as being paranoid, you'll also have your morals to think about and not have to think "... but it would also be really stupid not to have someone with the same issue tag along."