I understand the last sentence means he can’t be too careful. But how should I make sense of this bold に? If it was を, then it’s easier to understand.
Japanese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Japanese language. It only takes a minute to sign up.Sign up to join this community
As noted in the comment, this に can be understood as the common place indicator and 警戒と注意 as an abstract place. Essentially it means the same as に関して here. So literally, In the realm of caution and attention, doing too much does not exist.
Using を is possible, but then inserting a comma looks odd. It should be 警戒と注意をしすぎということはないだろう. This is probably because the verb-object relationship is felt stronger than topic-verb relationship in case of using に.