To demur is to:

To demur means to raise an objection or express hesitation about something. It signifies a reluctance or refusal to accept a particular proposition or idea, illustrating a critical or cautious attitude towards a situation. This term is often used in contexts where someone might question or challenge a proposal or point of view, indicating their disagreement or need for further consideration before acquiescing.

In contrast, the other options do not capture the essence of this verb. Agreeing without hesitation aligns more with acceptance rather than objection. Supporting an opinion fervently suggests a strong endorsement, which opposes the idea of demurring. Remaining indifferent implies a lack of concern or consideration, which does not reflect the act of questioning or objecting inherent in demur. Therefore, the choice of "take exception to something" accurately conveys the meaning of demur.