My advice is to be the example of change, and do it publicly. No matter your calling, go with the missionaries, or ward missionaries into the homes of the people, encourage them to participate (don’t condemn them). The important thing here though isn’t the message you are bringing, but the example. When enough members have seen you in their homes word will spread about what you’re doing. In time they will want to live up to your example.

Also, when somebody accepts a calling, congratulate and thank them perfusely. Don’t mention the sense of apathy, just encourage them.

Instead of bringing up the apathy on the pulpit, tell the ward the things they’re good at. Think of it as positive reinforcement. Let them begin seeing themselves as a good, industrious ward in their own eyes, and they will again, want to change to fit the new standard.