There was a lot of controversy in the last couple of years about an attempt by the government of San Francisco to impose their nihilistic requirements for birth control and abortion insurance coverage for all employers in the city. Catholic Charities fought this on religious grounds, but lost in court. The court cited the factors I listed above in determining that CC is not a religious organization, and after reviewing the facts of the case I had to agree with the court on that one.
"...and does not provide charitable services primarily to Catholics."
I assume you are not a Catholic if you think that a Catholic charity should provide charitable services primarily to Catholics.