"Wintermas" is supposed to the the secular substitute to Christmas. However, the -mas comes from Mass, a religious term, and while it would be winter in the northern hemisphere, it would be summer in the southern hemisphere.
Where are the other religious groups? Where are the Jews, the Muslims, the Hindus, the various pagans, and who knows what else?
Reflective of the author's complete inability to understand anyone actually believes in any (version of) god than his specific variety of Christian one, and isn't just non-Christian out of some need to rebel. It came up in Left Behind as well, that everyone not Real True Christian was happy to abandon their religion as soon as the evil world government told them to.
How does the global atheocracy keep religious faith illegal and make it shrink into obscurity? Think about it. Muslim terrorist groups in the Middle East would lay down their arms and submit. Neglecting that factor, they probably assume Christians wouldn't fight back: which isn't realistic either. Plutarcho Calles attempted to outlaw Christianity in Mexico in the 1920's and that spawned the Cristero War.
At the end of the second book, the "good guys" pray to God for a repeat of the slaughter of the firstborn out of the Old Testament, and the beginning of the third book indicates it's worldwide, not just targeting agents of the "evil" atheist government. Given how well the world is supposed to be doing, and known demographic trends - to wit, that as populations grow more affluent, they tend to have fewer children, for a variety of reasons - then it's very likely Paul and his cult just nearly committed a full-on Gendercide.