Anxiety can have physiological causes, e.g. stemming from GI disturbances, or hormonal causes. Not knowing your medical history, and due to the fact that nothing is ever simple in our bodies, it's difficult to pinpoint the cause of your anxiety to a specific event. If you feel anxious around your periods when you cleanse, perhaps move the cleanse to a time that does not fall on these days.
Personally, I think that people who are more sensitive in general, seem to also experience different things during fasts, or cleanses. I myself had anxiety attacks during the bowel cleanse, and could not sleep during fasts. A plausible cause is that we disrupt what our body is used to and would like to continue to function with - homeostasis. So the body does whatever it can to restore this equilibrium.
Another thought is that our GI tract has what we call an "enteric brain", and this area of our body contains a lot of chemical substances (peptides, neurotransmitters, etc.)that are also found in the brain. So, for instance, stomach problems may lead to anxiety, perhaps because a certain chemical (cholecystokinin), used to digest food there, is also used in the brain to trigger certain areas that may result in anxiety.
Just as an example. Observe your body's responses, and perhaps keep a journal, to find out what event correlate with the anxiety. You may not be able to find the actual cause for sure, but you will be able to identify correlates to avoid in the future with your bowel cleanses. That's what really matters!