I do not know if there is a connection as McAllister was very common name in County Antrim. Alexander McAllister and his wife Catherine Moore settled in Bromley Township in Renfrew, Ontario, Canada. They had six childen : Ann, Mary, John, James, Catherine and Alexander. I know they were from County Antrim and Anglican. I have no idea about parents or when family emigrated. DNA is R1b1a2 (also called M269). We have a 37-exact match with a McAllister family who emigrated to USA.
I would be happy to share info. Barbara