The Catholic Church is trying to deny its lower income workers access to contraception, Catholic or not.
The convoluted notion that providing money to a broadbased insurance pool that may be used to cover contraception is not actually using or forcing anyone to use contraception. Maybe all the "premiums" paid by the Catholic church go to the costs associated with single mothers and childcare, while the premiums of other employers can be used for contraception.
At the core, it's not about where the Catholic employer money goes, it's about trying to use political force to defund it for poor people. Refusing to pay for an insurance plan that provides such coverage does more to coerce the poor than anything the government is doing.