No, they should not. Rancher Support does not in any way require data that could be classified as sensitive (e.g., PII, PHI) to look into issues and troubleshoot toward resolution. The type of logs requested and collected by Rancher Support for troubleshooting has been described under What kind of logs are collected by Rancher Support?.
Also, Rancher Support does not have access to any data that a customer org does not want for it to have access to. Customers can further make sure that any of the logs requested by Rancher Support are sanitized to the necessary extent of their own company's InfoSec requirements before such logs are shared with Rancher Support.