As I understand it,
Baptists and Roman Catholics et al . . . maybe Lutherans, Presbyterians and Methodists, too.
both tend to cound on their membership rolls . . . folks who have long since stopped attending.
That has to inflate things somewhat.
In our Presbyterian church (and most every other church you mentioned) only active members are included. The people in the pews on Sunday are who are being counted as members.
In fact, when you move you transfer your membership from the previous Presbyterian church to the new one. There's no place for padding the numbers.
It's not about numbers. 8~)
Quite incorrect — US gov census will ask people what they believe in and that is then marked. This is not Scandanavian style.