I would absolutely require a caregiver to be fully vaccinated – and also that they not work if they knew they were sick. PALS are very vulnerable and that vulnerability needs to be acknowledged and addressed.
My husband passed away from ALS in 2014, so he did not have to deal with COVID. However, there were other contagious illnesses around, and one time a caregiver came in with bad bug. My husband got sick, the bug developed into pneumonia, and my husband had to be hospitalized. His extended illness and hospitalization resulted in a significant and horrible progression in his disease. After that I was MUCH more careful and I would not allow people who seemed sick, even family, to be in the same room as he was.