No. Caring is concern. Caution is taking care, avoiding danger.
The opposite of caution is carelessness. The opposite of caring could be apathy.
The opposite of 'caring' is 'uncaring'.
The opposite of caution (taking care) could be carelessness or recklessness.
Not caring, uncaring, careless
concern, caution, regard, interest, worry
Caring, attentive.
cautious
The opposite of apathy (not caring) could be concern, or interest.
The opposite could be gentle, or compassionate.
uncaring
caring passionate
Stoicism is impassive, indifferent. The opposite is care, concern, feeling, interested, passionate, sensitive, caring
interest, concern, caring, regard, compassion