The Standard for Those in Public Ministry
I am Catholic, but my wife is not, and I am wondering if I am able to be an extraordinary minister of Holy Communion, since we were not married in the Church.
The issue is not that your wife is a non-Catholic. The issue is that your marriage is not recognized by the Church.
Catholics chosen for positions in public ministry are expected to live in accordance with the teachings of the Church. Otherwise it sends a mixed message to the faithful about the importance of Church teaching.
I would recommend speaking to your parish priest about validating your marriage in the Church.