Because in our founding we explicitly said that we won't be a Christian nation legally, so having either "In God We Trust" and Christmas as a federal holiday are both bad, as they violate the first amendment.
No, they don't.
The interpretation of the Establishment clause that prohibits those ideas is a very marginal one that has never held any sway in interpretation of the clause by the courts, outside of Justice Ginsburg's radical dreams, and the idea that the Federal Government would not recognize God or was founded as a purely secular state by the founders is utterly ridiculous and by evidence allow me to present the reverse of the
Great Seal of the United States:
Why is this evidence against you claim? Firstly, the reverse of the Great Seal contains imagery that is EXPLICITLY Christian and was understood as explicitly Christian at the time it was adopted. That imagery? The Eye of Providence within a Triangle.
What, you thought that was some symbol of the Illuminati or just some generic symbol for a generic non-sectarian idea of God or some symbol of Freemasonry? No, the Eye of Providence, especially when surrounded by an Triangle is explicitly a reference to the Orthodox Christian view of God, with the triangle representing the Christian idea of the Trinity.
As to it's use by Freemasons, you have the connection backwards. Freemasons (and the Illuminati) adopted the Eye of Providence Symbol in the 1790s, whereas the United States adopted it in the 1780s. In short, both the Illuminati and Freemasons took up the symbol due to it's association with the United States and what the new country represented, rather than the United State adopting it because of some conspiracy theory.
Secondly, to further support the idea that the Founders who adopted and wrote the Establishment clause had no care about referencing God in official symbols is the Latin phrase "Annuit Coeptis". Meaning "Favors our undertaking." While it's popularly translated as "Providence favors our undertaking" due to it being understood as being linked to the Eye of Providence, as I already showed at the time of it's adoption the "Eye of Providence" was understood to be a reference to God as understood by Christianity, thus, the translation can be equally understood as "God favors our undertaking."