I don't know if my dad ever joined SAR. I have not. My wife researched diligently for her DAR qualifications and was rejected for having a Quaker in her lineage. After months of effort, she just dropped it entirely.
It should be easy to find out if your father was ever a member of the SAR. I think they have records of everyone who ever belonged. I could have some Quaker ancestors way back (but not the ancestor I joined under, who was a Scots-Irish Presbyterian)...but I haven’t verified the Quaker bit. My Confederate great-great-grandfather later belonged to a pacifist denomination but I don’t know if he was a member during the war.