Is it common for memories of a previous trauma (abuse) to be re-experienced and cause anxiety while processing a new trauma (rape) in therapy?

Yes, not uncommon. Pleased to hear you are taking active steps for your health and wellbeing to resolve the impact of these events. Because our brain is linked by common pathways it is not uncommon for memories of trauma to be linked. Be sure to discuss these experiences with your therapist as identifying linked memory/event "hotspots" may be important for overall treatment outcomes.