On this essay I worked with a counselor who practices in the South, and he said one of his problems with mindfulness exercises in the Bible Belt is that his clients often think he's asking them to (heaven forbid) meditate. Which is Eastern religion, and therefore unacceptable. So he often mentions that prayer can be a useful form of mindfulness.
A key difference between DBT and REBT/CBT is that we aren't disputing the emotions, or identifying/disputing the beliefs behind them necessarily. We are recognizing and accepting them, then managing our reactions. It's not really a conflict, anymore than REBT and CBT are in conflict, it's more a difference in the way one gets to the desired outcome of more effective management of how we respond to our own emotions.
A couple of times people have said to me that REBT seems to be denying or suppressing emotions. People who know more about REBT/CBT than I do usually respond that we are not doing so, we are simply changing how we respond to the emotions. But this approach seems to be more accepting of 'negative' emotions.
A big part of this is to simply slow down as you identify what you're feeling and how you're reacting. Just the process alone can help reduce the overwhelmed feeling we often get when life presses down. Sometimes the emotion passes and we're back on an even keel. It can be useful then to do a rational disputation of the underlying beliefs. Relax the body, and the mind will follow.