Hi, I was in a similar situation years ago, divorcing a Scientologist on staff at the local org and having two young children. The best strategy to prevent the child being indoctrinated into the cult is to have primary physical custody, and thereby, primary power of decision. The winning argument to make is that it is in the best interests of the child, and to be able to successfully argue for that for more reasons than only exposure to Scientology. If your ex is going to try to "disconnect" you from access to the child and argue for that, you could use that to your advantage and make an accepted and persuasive point, i.e., "the doctrine of the friendly parent", being, "that parent who will encourage and support a good relationship between the child and the opposite parent is the better parent". While family law differs in some respects from state to state, this principle is universal.
I had the drive and skills to study family law and become something of an acknowledged expert, and represented myself in court ("pro se"). I gained transfer of custody to me. In court, my ex had the backing of Scientology to bring in a Scientology friend to testify as an "educator" on her behalf. I successfully challenged her credentials and her credibility, as part of prevailing over my ex's team of 3 attorneys.
You may fare better with representation if you feel this is too much of a challenge, but if so I would recommend finding representation with someone who seems to really care about making this happen for you and your child, and isn't too arrogant to incorporate my suggestions into their strategy.
Try to always keep in mind, even though things can get stressful and you won't win every battle, in the big picture, in the long run, everything will be ok. Any upsetting moment or situation is not "how things will be forever", although it might feel that threatening for that moment.
