If this happens, I will seriously consider becoming Muslim, and urging other irreligious people I know to consider doing the same, to dilute the database. I'd remain an atheist, but I'd be a Muslim atheist instead of a Christian atheist. I'd buy a Quran and read it once, then put it on the shelf and not believe it, replacing the Bible that is currently on my shelf not being believed. For local charity giving, I'd direct that to a local mosque instead of a local church.
Only 0.9% of people in the United States are Muslim. Atheists and agnostics make up about 7%, so if a large fraction of atheists and agnostics registered as Muslims, it would greatly dilute the database. There are also a substantial number who believe in some sort of spirituality but not in traditional gods, and quite a few people who believe in gods but as a personal thing and not as part of an organized religion. All of these together make up about 20% of the population. If a lot of those people would register as Muslims, it would really really dilute the database.