Members are angry about the cardinal's recent comments about the gay community and the Ku Klux Klan.
The cardinal was commenting on the possibility that next summer's gay pride parade might interfere with worship at a Catholic church.
He has since softened his remarks but hasn't withdrawn them.
The ad says "gay is not like the KKK."
The organization said it fights for lesbian, gay, bisexual and transgender rights.
The organization calls the cardinal's statements an "example of religious bigotry."