I doubt it, immensely. Most churches/synagogues are run informally at best. The larger ones might have a manager or executive director at best, but that’s likely to be the exception, not the rule.
That means that the church’s finances will be informally kept. And likely only one person can make sense of them.
Now, that’s on an individual level. The BIG churches (i.e. the Baptist Church of America or whatever it’s called), the Mormons (LDS church), etc. WILL have very complete finance information. (Not the Jews, there is not one central Jewish coordinating agency).
But what would happen if you wanted the Baptists or Mormons to open their books for examination? First they would ask “why” – then they would stall, then they would obfuscate, and maybe a year later they would dribble out some information.
Bottom line: they see themselves as private and it’s none of your damn business about their finances.