Is mbsr training recommended for patients suffering clinical depression, mild chronic depression, or high levels of stress and anxiety?

It can be: Very helpful for some but if severe enough should not replace professional evaluation and management.

Not everyone: I recommend mbsr training to many of my patients. Recommendations are very individual, since severely depressed people may not be able to attend well to the process, or silent meditation may result in losing one's self in self-deprecating/negative thinking. Moderate depression is quite different though -- there is even mindfulness-based cbt for depression. Mbsr can be very helpful in anxiety!