A number of people who left religious cults and abusive churches lost their faith and trust in God. However, there are also many people who were able to maintain their faith and trust in God.
Why does it happen that some people lose their trust in God and some do not? I think it depends on their experience in these groups. Probably, people who experienced more abuse "in the name of God" tend to lose their trust in God more easily than those who did not.
After I spent 5 years in a cult, I had a desire to leave and to join a Christian church. I still had faith in God at that time though I had serious problems with the cult leaders. However, I did not leave. I left only 5 years later. By that time, I completely lost faith in God. Those 5 years were filled with the leaders' abuses. They always told that they carried out God's will. I wish I had left much earlier. Then, I would not have so many spiritual problems.
There are so many people who left abusive churches and who lost their faith in God. This is a real problem.