Jesus didn't come to make us moral or moralistic. Jesus came to transform us - the morals come with the transformation.
Mistaking Christianity for moralism is common. The equation of the two happens when cultural Christianity replaces really following the Christ of Christianity.
What's true about real followers is that they're moral people (or on their way to becoming moral people). But the morals don't come from an external conformity to a set of behavioral standards. The morals come from a deep-seated, deep-rooted change at the level of the heart where they want what's moral, what's good.
Last thought: I'm not dogging morals here. They're good. They're right. They reflect God's standards and desires for how the world should operate. And for sure, in society we'd rather have morality than immorality, but don't think that it will suffice as a substitute for truly following.