Spoiler***
i dont know how to do the hidden message stuff so ill just say that the institute DOES in fact fight with the minutemen.. however if you have high charisma you can resolve things peacefully... otherwise the minutemen will attack you also.
You can convince the minutemen that they are wrong about the institute and then they stand down (but only with high charisma.. if the check fails they attack you)
youll get questioned about it by garvey next time you see him.