> But every single citizen has to inform the government where they live and their religion. You also have to inform your boss of your religion.

That depends on the religion. For a bit more context (read the full history in [1]): As part of the 1800s separation between state and church, the major ones (Catholic and Evangelic-Lutheran) got the right to a percentage of employed people's wages as a sort of "membership fee". This gets deducted by the employer out of your paycheck and collected by the tax office, then distributed to the church you're a member of. Over the years, the right to collect these taxes expanded by quite a number, although currently only the Roman Catholic, Old Catholic, Evangelic-Lutheran, Free Protestant and Jewish synagogues use that right.

In real life, no one but HR at onboarding cares which religion you specify.

Also note, this is not exclusive to Germany. Italy, Sweden, Austria, Finland, Denmark and Switzerland all have a similar system.

[1] https://de.wikipedia.org/wiki/Kirchensteuer_(Deutschland)

I understand that it's related to taxes and that it's not exclusive to Germany (that's just the one I'm most familiar with). But there are better ways to do this that don't involve the government or my employer. These things violate my personal privacy far beyond what an advertising company does, or at least have an actual effect on my life.

I also think you're massively underestimating how much people care, especially in an increasingly secular Europe, even in very liberal cities like Berlin. And in small companies, there is no HR.

Why are Germans ok with registering their religion with their government after the government rounded up everyone of a certain religion and killed them?

Because those religions wants to collect taxes, to do so they register their members so that they automatically can take a part of your paycheck. A bigger question is why Americans are fine with the state registering their race given how much history of racial abuse they have.