I get that they are saying that the rats were wary of the snakes, but it feels like they are saying that the rats took care of the snakes.
Well, look to the reflexive pronoun se here. If the rats were taking care of the snakes, we might say that les cuidaban — "they guarded them." But instead we're saying that the rats se cuidaban — "they guarded themselves."
They guarded themselves (se cuidaban) against (de) what? Against the snakes (de las serpientes).
A similar use of the reflexive verb cuidarse would be if I told you ¡Cuidate de las serpientes! — "Guard yourself against the snakes!" or colloquially, "Watch out for snakes!"
If you wanted to say that the rats took care of the snakes, you'd say los ratones cuidaban a las serpientes; if you were talking about the snakes like they were real human people you'd say los ratones les cuidaban a las serpientes. Notice the change from cuidar de (guarding "away from") to cuidar a (guarding "toward"), which metaphorically matches the rats' posture in re the snakes.
By the way, if you wanted to say that the rats took care of the snakes while being faithful to the ambiguous English meaning of "take care of", you might say that los ratones se encargaron de las serpientes, which says something like "the rats (took charge of/took on/took responsibility for) the snakes," without being overly specific about what responsibility we're talking about here, exactly. (But I'm not super confident about this paragraph. I should have paid more attention to the subtitles in Breaking Bad. Anyone feel like leaving a comment to correct me? ;))
UPDATE after a well-intentioned but sense-changing edit by someone else: It appears that my use of les above may be a case of leísmo and may vary by region/dialect/training. (I am a non-native speaker who learned in high school in the eastern U.S.) Anyway, I claim that los ratones cuidaban a las serpientes would be clearly correct; los ratones les cuidaban a las serpientes sounds correct in "my" dialect if we're pretending that the snakes are funny animals in the Beatrix Potter tradition; ¿Qué hacían los ratones con las serpientes? Las cuidaban. would be correct; and repeating the direct object los ratones las cuidaban a las serpientes would be unnatural in anyone's dialect AFAIK.