I think this is an NTP thing, although the INTPs may mostly do this online. At any rate, as someone who may also be an ambiverted ENTP, I would like to weigh in this. I'll preface this by saying that there are times when I too find the behavior of going after sacred cows irritating, usually when they have nothing of value to replace it with.
I think there is usually more to it than just doing it for fun (although they may derive enjoyment from the process). Personally, when in my late adolescence, I started to feel betrayed by (earlier in life) trusting in ideas imposed on me by authority figures that my own experiences led me to question. If I found that the authority figures can't justify their ideas, that only makes the anger and sense of betrayal worse. Later, in early adulthood, this became a tendency to disparage or have no respect for ideas people believed without knowing why they believed them. I think there is a good chance a lot of NTPs go through something similar. This internal feeling might manifest in a desire to go after those ideas whenever they are expressed. I think the NTP will often feel that they are doing something good by trying to lead others away from falsehood.
As I got older, I found that this wasn't always a worthy enterprise to engage in, and even if it was, I've found that often a less confrontational approach is more likely to be effective.
Also, keep in mind that the "wrong Ideas" the NTP may have a distaste for do not necessarily need to be religion. In my particular case, religion was not a big part of that at all.