Essentially, the HMS mandate requires all Catholic organizations to pay for birth control. Birth control is something they consider "gravely immoral". These organizations employ catholics and non-catholics alike and make no pretense about their moral values.
This view of life is something shared by many non-catholics, Ghandi being one of the more prominent figures.
By requiring them to pay for these "health services" they are complying with immoral action and are therefore being forced to act immorally.
I appreciate Catholics for their consistent view of life. You don't have to agree with them to see that mandate as a problem. I value humanity, life and consistent moral values.
It's the same reason I appreciate my friends who are pure hedonists. They are consistent, they don't act like they are searching for anything other than pleasure. If they can use you or something else to increase their pleasure, they will. Consistency being the key word.