Frank likely observed the patient's behaviors and used cultural intelligence to determine that Clara may be more comfortable with an NA whose gender fits more closely to Clara than his own.
The patient's chart should not include the patient's socioeconomic background unless it is specifically pertinent to the care being administered. Age difference between patients should not create an insurmountable barrier to communication (adult can work with ages from children to geriatrics!). Lastly, it is not good practice to advertently assume the patient's gender identity and then impose one's own beliefs based on that assumption. This is not to say assuming one's culture is the best practice either however!