It's a subtle difference. Churchgoers don't get a free pass to break the law. The establishment simply is immune to regulation of any kind attempted to be placed upon the organization itself by congress.
It's not obvious that this is what was meant by 1st amendment. Other interpretation is that congress simply can't make laws that apply exclusively to religious establishments.
EDIT: I must add that the interpretation you mentioned is undoubtedly the "canonical" one in public's mind, so the situation is unlikely to change soon.
This interpretation would be compatible with taxing churches (as long as they are all taxed equally).
It was certainly my view before I studied the topic.
It turns out that congress is not allowed to legislate religious establishments at all.
Are you arguing that my congregation should be immune from any restrictions being placed on us for worshipping our god by slowly killing everyone around us who does not share our view , because we operate outside of the law ?
What Congress isn't allowed to do is pass a law stating "no religious organizations in the US are allowed to practice human sacrifice." But you still wouldn't be able to appease Xanakto the Moon God because Congress is still allowed to make murder illegal in general, just not exclusively in the context of religious practice.
And, ironically, the reason religious organizations are included at all is the belief that taxing them would provide a means by which governments could interfere with religion in violation of the First Amendment.
Arguably, that just means you can't pass laws that are directed towards / against religion. Not that religion is above the law. See Lemon Test: https://en.wikipedia.org/wiki/Lemon_v._Kurtzman#Lemon_test
According to this interpretation, church taxes (like the ones still present in some European countries) are unlawful, as is denying churches ability to gather their own donations. But churches still should pay same taxes that apply to other NGOs.