Catholic charities of all kinds are ceasing to be so. In some cases they like to parade their Catholic 'heritage' when asking for Catholic money. It would be useful to have proper criteria for Catholic organisations, which we could use to weed out the fakes.
First: on claims to a Catholic 'ethos' or 'values'.
A charity can obviously claim to have a Catholic 'ethos', or say that it is founded and informed by Catholic values or a Catholic perspective. This will effect who wants to be a donor, a trustee, or a beneficiary. So although one might think that the mere claim to a Catholic ethos or Catholic values is a rather feeble effort for a 'Catholic' institution, actually it is of great significance, because the claim - on websites and so on - itself tends to create such an ethos. And it is amazing how many formerly Catholic charities decline to make such a claim.
Second: on cooperation with evil.
We need to go beyond this, of course, and say what effect Catholic values have on the running of the institution. So it would be reasonable to say, as a result of the ethos and values, there are certain things the charity will not do: obviously formal cooperation in intrinsically evil actions, but also proximate material cooperation in intrinsically evil (or gravely evil) actions. Catholic teaching gives us a list of intrinsically evil actions to use. So a Catholic institution wouldn't employ a person to expedite abortions (formal cooperation) or have a condom machine (proximate material cooperation). It might allow employees to misuse their freedom of speech to speak against the Church or the moral law, since this is a more distant material cooperation, but it would seek to minimise this and counteract the evil effects of it.
Third: on Catholic aims.
The second point is merely negative. So, the next step is to say that a Catholic charity is one which has Catholic aims. These would be of the form: 'To give glory to God by doing X.' X could be anything, but many formerly Catholic institutions would find it deeply embarrassing to put it like that in their self description, and I think that should rule them out. We can take it a step further and say: a Catholic institution is never concerned merely with the bodily or financial welfare of its beneficiaries (or staff), but also with their spiritual welfare. And then we can ask: what do you do to promote this spiritual welfare? The answer should include, I would suggest: by performing our tasks in the spirit of the service of Christ in the persons of our beneficiaries; by prayer in common; by marking the Church's seasons and feasts; by having Mass said in or specifically for the institution at least several times a year.
None of this will get anyone into trouble with the non-discrimination or harassment laws. But it would make for a genuinely Catholic institution.