In general, neither exposure to or recovery from an infectious disease is a contraindication or precaution to vaccination. In particular, recovery from varicella (chickenpox) is not a reason to withhold a live vaccine, such as MMR.
COVID-19 is the exception to this general rule. CDC recommends that routine vaccination should be deferred for persons with suspected or confirmed COVID-19, regardless of symptoms, until criteria have been met for them to discontinue isolation. The reason for this exception is that vaccination visits for these individuals should be postponed to avoid exposing healthcare personnel and other patients to the virus that causes COVID-19.