The symbiote has a very specific approach to take over the host.
Ultimately, it is a parasite. It pretends to be a symbiotic (i.e. mutually beneficial) relationship, to further its goal of consuming the host. Although I do think that for the symbiote, its goal is more to have the host consumed by anger, rather than the symbiote literally consuming (i.e. eating) the host.
First, the symbiote gives you what you want. Brock felt powerless to improve his life, so therefore the symbiote gave him the means to be powerful.
Peter, while already trying to be a hero, feels like he's not good enough (this may be a consequence of having grown up as an undervalued nerd). The symbiote enhanced Peter's existing abilities, so that he felt more capable of being a hero.
The goal is the same: Brock and Peter accept the symbiote, because it makes them better.
Secondly, over time, the symbiote subtly alters the host's behavior. In both cases, it presented as increased aggression.
Peter is a good guy. The symbiote can't change him over night. Not only that, Peter is also self-aware enough that he starts realizing something is wrong.
The same is not true for Brock. First of all, he enjoys the aggression, as it is in line with his own character even before he met the symbiote.
The main difference between Brock and Peter is that Brock willingly succumbs to the anger and aggression that the symbiote introduces (or exacerbates), whereas Peter is driven by his principles and therefore objects to the increased aggression.
As a direct answer to your question:
Why did it not turn Peter into these same monsters?
It did. It just happened much more slowly, because Peter is innately a good person, whereas Brock is not (I can't speak to Cassidy).
Not only did it happen more slowly, but Peter willingly rejected the symbiote when it proved to be a danger, whereas Brock embraced it fully even when told about the dangers.
If the symbiote tried to change Peter as fast as it did Brock, then Peter would have immediately protested and rejected the symbiote. It needed to be subtle, and therefore took its time.
The symbiote is a con man. First he gets his foot in the door, makes you trust him, and then it silently siphons away everything you have.
The smarter (in this case: morally good) you are, the longer it takes for the con man to convince you that he's not after your money.