Christian nationalism is a bad idea, and at some level, it's everyone's responsibility to combat bad ideas.
However, the underlying bad idea is not Christian nationalism per se, but rather the idea that it should be socially acceptable to believe things based on undemocratically sourced evidence, e.g. messages from a prophet or "holy" book.
But in that light, Christians make bad partners in combating Christian nationalism, because they depend on the social acceptance of undemocratic evidence.
I'd like to make some thing clear that I think a lot of people don't get: The thing that makes Christian nationalism a bad idea is the Christianity. What doesn't make it bad is the desire for a national ideology.
Because ultimately, every nation needs some type of national ideology. If you think about it, that's actually what the constitution is supposed to provide. Humans can't form a community together unless they agree upon some core things.
What we all need to do is find the right core things, and then convince everyone, through logical, thoughtful dialogue, that they are the right things. That's the only way that we'll get the world we all need. It's not by embracing tolerance of all religions or ideas. It's by only tolerating beliefs that stem from democratically observable evidence.