The moral concept at play here is one of degree of moral cooperation. The old Catholic Encyclopedia provides a nice summary under it's entry for "Accomplice":
A term generally employed to designate a partner in some form of evildoing. An accomplice is one who cooperates in some way in the wrongful activity of another who is accounted the principal. From the viewpoint of the moral theologian not every such species of association is straightway to be adjudged unlawful. It is necessary to distinguish first of all between formal and material cooperation. To formally cooperate in the sin of another is to be associated with him in the performance of a bad deed in so far forth as it is bad, that is, to share in the perverse frame of mind of that other. On the contrary, to materially cooperate in another's crime is to participate in the action so far as its physical entity is concerned, but not in so far as it is motived by the malice of the principal in the case. For example, to persuade another to absent himself without reason from Mass on Sunday would be an instance of formal cooperation. To sell a person in an ordinary business transaction a revolver which he presently uses to kill himself is a case of material cooperation. Then it must be borne in mind that the cooperation may be described as proximate or remote in proportion to the closeness of relation between the action of the principal and that of his helper. The teaching with regard to this subject-matter is very plain, and may be stated in this wise: Formal cooperation is never lawful, since it presupposes a manifestly sinful attitude on the part of the will of the accomplice. Material complicity is held to be justified when it is brought about by an action which is in itself either morally good or at any rate indifferent, and when there is a sufficient reason for permitting on the part of another the sin which is a consequence of the action.With this in mind, I think it should be clear there is a big difference for an organization which considers contraception to be immoral between providing employees with health care coverage specifically for buying contraception and providing them with money which they can choose to use for anything they want. The former clearly restricts their actions only to getting something which, according to a Catholic view, is immoral anyway. The latter is simply the just act of paying a worker for his labor, and leaves the worker in charge of deciding how to spend that money. Even if in both cases the worker ends up getting birth control, the proximity of the employer to the buying of birth control is clearly much greater with the contraception mandate than with simply providing his workers with money.
I'd argue that this distinction is actually really clear to us even on subjects which don't involve any clearly immoral action if we start applying it to things that we think of as strictly option. Suppose, for example, an employer provided bicycle coverage to all his employees. Any employee could get a free bicycle. Of course, if you don't want a bicycle, you don't have to get one. People strongly in favor of bicycles might think this was just awesome, but a lot of employees might see this as interfering and overly benefiting the people who are bicycle fanatics. However, a lot of people might see this as a inconsequential "perk" that the company offers and not worry about it too much, though they would certainly see the company as encouraging cycling.
Now let's apply the same model to something that is legal but a little more controversial. An employer announces that they will provide "2nd Amendment Coverage" to all their employees. Any employee who wants can get a "free" Glock 9mm pistol as part of this coverage. He or she can also get unlimited ammunition. Of course, no one is required to get a gun, and the company is not encouraging anyone to do anything illegal or dangerous with these guns. Guns are perfectly legal, and any employee who wanted to could obviously go out and buy a Glock and ammunition for it with his salary if he wanted. However, I think basically everyone would agree that this "2nd Amendment Coverage" would represent the company far more directly being involved in gun ownership and gun promotion than a company which simply payed its workers and didn't prevent them from buying guns with their salaries. This employer would be engaged in "material cooperation" with gun ownership and gun culture in a way that other employers were not.