AllalongWatch - congratulations on your pregnancy! That's wonderful news for you and your wife.
We all need hope and belief - in something (even if it is the belief that there is no god and there is only ourselves). And it seems like your wife is spiritually minded and has a belief in god - it is not at all unusual for people when they have children to question their faith more. I did, and the reverse happened, it took me away from the witnesses. So don't assume this is a bad thing.
However, it depends on her emotional state. Obviously I don't know your wife, you or the ins and outs. But I am going to offer my suggestions here and see how they feel for you.
Pregnancy is an emotional time anyway for all the good expected reasons and for all the hormonal reasons - ha ha (for me it was like having pmt for 9 months!). From what you have said and reading between the lines, in the past you have taken the intellectual dissuading approach and it seemed to work, until now. For this to come up again at this time I would appeal to the emotions and heart.
Just ask her lots of questions. Don't try and argue with her (tho don't throw logic out the window either). But rather ask her why she has started thinking about all of this now? There could be some much deeper emotions going on that are driving this. Is there fear about having a child (will she be a good mother? does she worry about creating a safe space in a 'bad world'? finances? security? birth? etc etc). You asked why the org is so insidious and one of the reasons is because it plays on people's fears. Fear pretty much drives most people (to various degrees) - so see if you can find out what she is really worried about. If you try and take away what she is trying to latch on to it will just make her feel more insecure.
Then talk positively about the type of environment (neutral) that you want to create for your child as a family. What kind of values do you want to instil? What kinds of principles, what is important to each of you, what can you both bring to the family (eg what are each of your strong points/gifts and how do you balance each other out?). Try and talk about a lot of positive aspects, it is important that she feels that these are within her and she is able to provide them for her child. The org plays on the 'helpless without us' aspect, help her see that she is more than capable of finding these answers from within, from you and from various sources.
You can do all this without even mentioning the witnesses - it doesn't need to be about them really at all. This is a beautiful time for you and your wife - enjoy!