Matrix Morpheus

An animal's basic instincts are considered types of thought that are activated without the need for proper cognition, although we are talking about humans in this case which makes you correct

*cognition
"cognitive thought" is redundant.

True enough, however cognitive thought is classified as the correct term

You can think without being cognitive, it basically revolves around a species abstract thought.

Used in this manner here it implies there may be types of thought that "aren't" cognitive.
Besides, no on ever says; 'here's a cognitive thought'...as opposed to 'here's a thought'.