Ann,
In my experience this is most commonly just a play on words, or a poorly worded statement. It isn't about behaviors that reflect Christ, but rather a matter of being nice to the point of appearing fake. Most people like sweets, but if you keep eating artificial sweetners, plain, they can become quite abrasive. Christ wasn't fake, He was genuine and at times frustrated and fiery. He said some very controversial things and very intentionally 'stirred the pot.'
Some people incorrectly think that as a Christian they need to be as nice as possible. In truth, they try too hard. Instead of relying on God to work through them, they try to be a ray of kindness all on their own. People see through it, it is a shallow kindness. Not the world-changing love of Christ.
Now I don't know you at all, so is this what they are telling you? I don't know. But I think the fact remains. They don't mean 'stop being so Christ-like'.