Correct Answer: Pay only lip service.

Solution : The third option is the correct choice.

Pay only lip service is the correct idiom for the context. It means to express support or agreement with words but not with actions, which fits the idea that some people claim to support a cause but don't do so.

The meanings of the other options are as follows:

• Are out of the frying pan onto the fire is an idiom that means going from a bad situation to an even worse one, which is not relevant in this context.
• Spare the rod and spoil the child is an idiom that means if you don't discipline or punish a child when necessary, they will become spoiled or misbehave. This idiom is unrelated to the context of supporting a cause.
• Mind their P's and Q's is an idiom that means to be very careful about one's behaviour or language, and it's unrelated to the context.