No, it shouldn't be illegal because of that true fact. Although, this is a Christian nation it is not a theocracy, and has tolerance for other religions and worldviews; therefore, the Constitution does not outlaw atheism as long as it does not interfere with the laws of the Constitution.
Let us also be clear that the origins of the Constitution were out of Christian values. If they were not, polygamy would be legal; blue laws would be unconstitutional; and it would be illegal to make Christmas, Easter, and other religious days national holidays. There is no official Ramadan day. Circumcision isn't mandatory.
And it is not a secularist nation either. If it were it would be antithetical to even place a protection on religious expression, because secularism denies the very existence of religion.
Now, can all that change? Can we become a totally secularist nation? Yes. But, first you would have to get rid of the 1st amendment to achieve the goal. And that can be done as there is allowance to overturn amendments. But I think you would be shattering the nature and culture of these United States to do such a thing.