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
cautious
Caring, attentive.
The opposite of apathy (not caring) could be concern, or interest.
uncaring
The opposite could be gentle, or compassionate.
caring passionate
Stoicism is impassive, indifferent. The opposite is care, concern, feeling, interested, passionate, sensitive, caring
interest, concern, caring, regard, compassion